Received 01/06/15
Single Lettter Representations of Natural Numbers
Inder J. Taneja1
Abstract. This is first work of its kind. It brings representations of natural numbers from 0 to 5000 in terms of single letter
a. For any value of letter a from 1 to 9, the result is always same. To bring these results, only basic operations as addition,
subtraction, multiplication and division are used. A separate section is dedicated to numbers with potentiation.
1. Introduction
Let us consider
f n (10) = 10n + 10n−1 + ... + 102 + 10 + 100 ,
For a ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}, we can write
af n (10) = aaa...a
| {z } ,
(n+1)−times
In particular,
aa = f 1 (10) = a10 + a
aa
.
a
aaa
=⇒111 :=
.
a
aaaa
=⇒1111 :=
.
a
aaaaa
.
=⇒11111 :=
a
=⇒11 :=
aaa = f 2 (10) = a102 + a10 + a
aaaa = f 3 (10) = a103 + a102 + a10 + a
aaaaa = f 4 (10) = a104 + a103 + a102 + a10 + a
......
For example, one can write
5=
aa − a
11 − 1
22 − 2
33 − 3
44 − 4
55 − 5
66 − 6
77 − 7
88 − 8
99 − 9
=
=
=
=
=
=
=
=
=
;
a+a
1+1
2+2
3+3
4+4
5+5
6+6
7+7
8+8
9+9
56 =
aaa + a
111 + 1
222 + 2
333 + 3
444 + 4
555 + 5
666 + 6
777 + 7
888 + 8
999 + 9
=
=
=
=
=
=
=
=
=
;
a+a
1+1
2+2
3+3
4+4
5+5
6+6
7+7
8+8
9+9
111 =
aaa
111
222
333
444
555
666
777
888
999
=
=
=
=
=
=
=
=
=
.
a
1
2
3
4
5
6
7
8
9
...
Detailed study on single digit representations can be seen in Taneja [11]. Here below are more examples:
717 = (1 + 1)11 − 11(1+1+1)
= 222 + 222 + 22/2
= 3(3+3) − 3 − 3 × 3
= 4 × (4 × 44 + 4) − 4 + 4/4 = (55 × (55 + 5 + 5) + 5 + 5)/5 = (6 × 6/(6 + 6))6 − 6 − 6
= 777 − 7 × 7 − 77/7
= 8 × 88 + (88 + 8 + 8)/8
= 9 × 9 × 9 − (99 + 9)/9.
923 = (1 + 1)(11−1) + 11 − 111 − 1 = 2 × (222 − 22) − 2/2
= 33 + 33 × 33 − 3/3
= 44 + 44 × (4 × 4 + 4) − 4/4 = 5 × (55 + 5) + (55 − 5 − 5)/5 = (6 + 6 + 6/6) × (66 + 6 − 6/6)
= 77 × (77 + 7)/7 − 7/7
= 888 + 8 + 8 + 8 + 88/8
= 9 × 99 + 9 + (99 + 99 + 9)/9.
Formerly, Professor of Mathematics (1978-2012), Universidade Federal de Santa Catarina, 88.040-900 Florianópolis, SC, Brazil. Before author
worked about three years (1976-1978) at affiliated colleges of Delhi University, Delhi, India. E-mail: [email protected].
1
1
2
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
995 = (11 − 1)(1+1+1) − (11 − 1)/(1 + 1) = 22 + 2 × (222 + 2) + 2/2
= 3 × 333 − 3 − 3/3
= 4 × (4 − 4 − 4) + 4 − 4/4
= 5 × (5 + 5) × (5 × 5 − 5) − 5 = 666 + 6 × 66 − 66 − 6/6
= (7 + 7) × (77 − 7) + 7 + 7 + 7/7 = 888 + 88 + 8 + 88/8
= 999 − (9 + 9 + 9 + 9)/9.
4
The representations of same numbers in terms of single letter a are as follows:
717 := ((aaa − a) × aa/(a + a) + aaa + a)/a.
923 := (aaaaa − aa − aa − aa − a − a)/(aa + a).
995 := (aaaa − aaa − a − a − a − a − a)/a.
We observe that in terms of single letter we may have to use more letters, but the results are valid for any value of
a ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}. Another advantage in working with single letter is that the representations are uniform.
2. Single Letter Representations
Here below are representations of natural numbers from 0 to 5000 using single letter a, where
a ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Four basic operations are used, i.e., addition, subtraction, multiplication and division. Numbers having potentiation are dealt
separately in next section. By no means, we can say that the representations given below are unique. There may have
alternative representations with less or more numbers of letters ”a”.
0 := a − a.
1 := a/a.
2 := (a + a)/a.
3 := (a + a + a)/a.
4 := (a + a + a + a)/a.
5 := (aa − a)/(a + a).
6 := (aa + a)/(a + a).
7 := (aa − a − a − a − a)/a.
8 := (aa − a − a − a)/a.
9 := (aa − a − a)/a.
10 := (aa − a)/a.
11 := aa/a.
12 := (aa + a)/a.
13 := (aa + a + a)/a.
14 := (aa + a + a + a)/a.
15 := (aa + a + a + a + a)/a.
16 := (aa + a + a + a + a + a)/a.
17 := (aa + a)/(a + a) + aa/a.
18 := (aa − a − a) × (a + a)/(a × a).
19 := (aa + aa − a − a − a)/a.
20 := (aa + aa − a − a)/a.
21 := (aa + aa − a)/a.
22 := (aa + aa)/a.
23 := (aa + aa + a)/a.
24 := (aa + aa + a + a)/a.
25 := (aa + aa + a + a + a)/a.
26 := (aa + a + a) × (a + a)/(a × a).
27 := ((aa + a + a) × (a + a)/a + a)/a.
28 := (aaa + a)/(a + a + a + a).
29 := ((aa − a) × (a + a + a)/a − a)/a.
30 := (aa − a) × (a + a + a)/(a × a).
31 := (aa + aa + aa − a − a)/a.
32 := (aa + aa + aa − a)/a.
33 := (aa + aa + aa)/a.
34 := (aa + aa + aa + a)/a.
35 := (aa + aa + aa + a + a)/a.
36 := (aa + a) × (a + a + a)/(a × a).
37 := aaa/(a + a + a).
38 := aaa/(a + a + a) + a/a.
39 := (aa + a + a) × (a + a + a)/(a × a).
40 := (a + a + a + a) × (aa − a)/(a × a).
41 := (aaa + aa + a)/(a + a + a).
42 := (aa + aa − a) × (a + a)/(a × a).
43 := ((a + a + a + a) × aa/a − a)/a.
44 := (a + a + a + a) × aa/(a × a).
45 := ((a + a + a + a) × aa/a + a)/a.
46 := (aa + aa + a) × (a + a)/(a × a).
47 := ((aa + aa + a) × (a + a)/a + a)/a.
48 := (a + a + a + a) × (aa + a)/(a × a).
49 := (aaa − aa − a − a)/(a + a).
50 := (aaa − aa)/(a + a).
51 := (aaa − aa + a + a)/(a + a).
52 := (aaa − aa)/(a + a) + (a + a)/a.
53 := (aaa − a)/(a + a) − (a + a)/a.
54 := (aaa − a − a − a)/(a + a).
55 := (aaa − a)/(a + a).
56 := (aaa + a)/(a + a).
57 := (aaa + a + a + a)/(a + a).
58 := (aaa + a)/(a + a) + (a + a)/a.
59 := ((aa × aa − a × a)/(a + a) − a)/a.
60 := (aa × aa/a − a)/(a + a).
61 := (aaa + aa)/(a + a).
62 := (aaa + aa + a + a)/(a + a).
63 := (aa + aa − a) × (a + a + a)/(a × a).
64 := ((aa + a) × aa/(a + a) − a − a)/a.
65 := ((aa + a) × aa/(a + a) − a)/a.
66 := (aa + a) × aa/((a + a) × a).
67 := (aaa + aa + aa + a)/(a + a).
68 := ((aa + a) × aa/(a + a) + a + a)/a.
69 := (aa + aa + a) × (a + a + a)/(a × a).
70 := ((aa + a) × (aa + a)/(a + a) − a − a)/a.
71 := ((aa + a) × (aa + a)/(a + a) − a)/a.
72 := (aa + a) × (aa + a)/((a + a) × a).
73 := (aaa/(a + a + a) × (a + a) − a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
74 := aaa/(a + a + a) × (a + a)/a.
75 := (aaa/(a + a + a) × (a + a) + a)/a.
76 := ((aa − a − a − a − a) × aa/a − a)/a.
77 := (aa − a − a − a − a) × aa/(a × a).
78 := (aaa − aa − aa − aa)/a.
79 := (aaa − aa − aa − aa + a)/a.
80 := (aa − a − a − a) × (aa − a)/(a × a).
81 := (aa − a − a) × (aa − a − a)/(a × a).
82 := ((aa − a − a) × (aa − a − a)/a + a)/a.
83 := ((aa + a) × (aa + a)/(a + a) + aa)/a.
84 := (a + a + a + a) × (aa + aa − a)/(a × a).
85 := (aaa/(a + a + a) × (a + a) + aa)/a.
87 := (aaa − aa − aa − a − a − a)/a.
87 := (aaa − aa − aa − a − a)/a.
88 := (aaa − aa − aa − a)/a.
89 := (aaa − aa − aa)/a.
90 := (aaa − aa − aa + a)/a.
91 := (aaa − aa − aa + a + a)/a.
92 := (aaa − aa − aa + a + a + a)/a.
93 := ((a − aa + a) × (a + a)/a + aaa)/a.
94 := (aaaa + aaa)/(aa + a + a).
95 := (aaa − aa − a − a − a − a − a)/a.
96 := (aaa − aa − a − a − a − a)/a.
97 := (aaa − aa − a − a − a)/a.
98 := (aaa − aa − a − a)/a.
99 := (aaa − aa − a)/a.
100 := (aaa − aa)/a.
101 := aaaa/aa.
102 := (aaaa + aa)/aa.
103 := (aaaa + aa + aa)/aa.
104 := (aaa − aa + a + a + a + a)/a.
105 := aaa/a − (aa + a)/(a + a).
106 := aaaa/aa + (aa − a)/(a + a).
107 := (aaa − a − a − a − a)/a.
108 := (aaa − a − a − a)/a.
109 := (aaa − a − a)/a.
110 := (aaa − a)/a.
111 := aaa/a.
112 := (aaa + a)/a.
113 := (aaa + a + a)/a.
114 := (aaa + a + a + a)/a.
115 := (aaa + a + a + a + a)/a.
116 := (aaa + a + a + a + a + a)/a.
117 := (aa + a)/(a + a) + aaa/a.
118 := ((aa × aa)/a − a − a − a)/a.
119 := ((aa × aa)/a − a − a)/a.
120 := ((aa × aa)/a − a)/a.
121 := aa × aa/(a × a).
122 := (aaa + aa)/a.
123 := (aaa + aa + a)/a.
124 := (aaa + aa + a + a)/a.
125 := (aaa + aa + a + a + a)/a.
126 := (aaa + aa + a + a + a + a)/a.
127 := (aaa + aa)/a + (aa − a)/(a + a).
128 := (aaa + aa)/a + (aa + a)/(a + a).
129 := ((aa + a) × aa/a − a − a − a)/a.
130 := ((aa + a) × aa/a − a − a)/a.
131 := ((aa + a) × aa/a − a)/a.
132 := (aa + a) × aa/(a × a).
133 := (aaa + aa + aa)/a.
134 := (aaa + aa + aa + a)/a.
135 := (aaa + aa + aa + a + a)/a.
136 := (aaa + aa + aa + a + a + a)/a.
137 := (aaaa + aaa + aa)/(aa − a − a).
138 := aaa/(a + a + a) + aaaa/aa.
139 := (aaaa + a)/(aa − a − a − a).
140 := (aa + a + a + a) × (aa − a)/(a × a).
141 := ((aa + a + a) × aa/a − a − a)/a.
142 := ((aa + a + a) × aa/a − a)/a.
143 := (aa + a + a) × aa/(a × a).
144 := (aa + a) × (aa + a)/(a × a).
145 := (aaa + aa + aa + aa + a)/a.
146 := (aaa + aa + aa + aa + a + a)/a.
147 := (aaa + aa + aa + aa + a + a + a)/a.
148 := aaa/(a + a + a) + aaa/a.
149 := aaa/(a + a + a) + (aaa + a)/a.
150 := (aaa − aa) × (a + a + a)/(a × (a + a)).
151 := (aaaa × (a + a + a)/aa − a)/(a + a).
152 := (aaaa × (a + a + a)/aa + a)/(a + a).
153 := ((aa + a + a + a) × aa/a − a)/a.
154 := ((aa + a) + a + a) × aa/(a × a).
155 := (aaa + aa + aa + aa + aa)/a.
156 := (aa + a + a) × (aa + a)/(a × a).
157 := ((aa + a + a) × (aa + a)/a + a)/a.
158 := ((aa + a + a) × (aa + a)/a + a + a)/a.
159 := ((aa + a + a) × (aa + a)/a + a + a + a)/a.
160 := (aaa + aaa + aaa − aa − a − a)/(a + a).
161 := (aaa × (a + a + a)/a − aa)/(a + a).
162 := (aaa + aa)/(a + a) + aaaa/aa.
163 := ((aa + a + a + a + a) × aa/a − a − a)/a.
164 := ((aa + a + a + a + a) × aa/a − a)/a.
165 := (aa + a + a + a + a) × aa/(a × a).
166 := (aaa + aaa + aaa − a)/(a + a).
167 := (aaa + aaa + aaa + a)/(a + a).
168 := (aa + a + a + a) × (aa + a)/(a × a).
169 := (aa + a + a) × (aa + a + a)/(a × a).
170 := (aaaa + aaaa − aa − a)/(aa + a + a).
171 := (aaaa + aaaa + a)/(aa + a + a).
172 := (aaa × (a + a + a)/a + aa)/(a + a).
173 := (aaa + aaa + aaa + aa + a + a)/(a + a).
174 := (aaa − aa − aa − a − a) × (a + a)/(a × a).
175 := (aa + aa − a) × (aaa − aa)/((aa + a) × a).
176 := (aaa − aa − aa − a) × (a + a)/(a × a).
177 := ((aa + a) × aa/(a + a) + aaa)/a.
178 := (aaa − aa − aa) × (a + a)/(a × a).
179 := ((aaa − aa − aa) × (aa + aa)/aa + a)/a.
180 := (aaaa/aa × (a + a) − aa − aa)/a.
181 := (aaaa/aa × (a + a) − aa − aa + a)/a.
182 := (aa + a + a + a) × (aa + a + a)/(a × a).
183 := (aaa + aa) × (a + a + a)/(a + a)/a.
184 := ((aaaa − a) × (a + a)/(aa + a) − a)/a.
185 := (aaaa − a) × (a + a)/(aa + a)/a.
186 := ((aaaa + aa) × (a + a)/(aa + a) − a)/a.
187 := (aaaa + aa) × (a + a)/(aa + a)/a.
188 := ((aaaa + aa) × (a + a)/(aa + a) + a)/a.
189 := (aaa + aaa − aa − aa − aa)/a.
190 := (aaaa/aa × (a + a) − aa − a)/a.
191 := (aaaa/aa × (a + a) − aa)/a.
192 := (aaaa/aa × (a + a) − aa + a)/a.
193 := ((aaaa + aa)/aa × (a + a) − aa)/a.
194 := (aaa − aa − a − a − a) × (a + a)/(a × a).
195 := ((aaa − aa − a − a) × (a + a)/a − a)/a.
196 := (aaa − aa − a − a) × (a + a)/(a × a).
197 := ((aaa − aa − a) × (a + a)/a − a)/a.
198 := (aaa − aa − a) × (a + a)/(a × a).
199 := (aaa + aaa − aa − aa − a)/a.
200 := (aaa − aa) × (a + a)/(a × a).
201 := (aaaa/aa × (a + a) − a)/a.
3
4
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
202 := aaaa/aa × (a + a)/a.
203 := (aaaa/aa × (a + a) + a)/a.
204 := (aaaa + aa)/aa × (a + a)/a.
205 := ((aaaa + aa)/aa × (a + a) + a)/a.
206 := (aaaa + aa + aa) × (a + a)/(aa × a).
207 := (aaa + aaa − aa − a − a − a − a)/a.
208 := (aaa + aaa − aa − a − a − a)/a.
209 := (aaa + aaa − aa − a − a)/a.
210 := (aaa + aaa − aa − a)/a.
211 := (aaa + aaa − aa)/a.
212 := (aaa × (a + a)/a − aa + a)/a.
213 := ((aaa + a) × (a + a)/a − aa)/a.
214 := (aaa − a − a − a − a) × (a + a)/(a × a).
215 := ((aaa − a − a − a) × (a + a)/a − a)/a.
216 := (aaa − a − a − a) × (a + a)/(a × a).
217 := ((aaa − a − a) × (a + a)/a − a)/a.
218 := (aaa − a − a) × (a + a)/(a × a).
219 := (aaa + aaa − a − a − a)/a.
220 := (aaa − a) × (a + a)/(a × a).
221 := (aaa + aaa − a)/a.
222 := (aaa + aaa)/a.
223 := (aaa + aaa + a)/a.
224 := (aaa + a) × (a + a)/(a × a).
225 := ((aaa + a) × (a + a)/a + a)/a.
226 := (aaa + a + a) × (a + a)/(a × a).
227 := ((aaa + a + a) × (a + a)/a + a)/a.
228 := (aaa + a + a + a) × (a + a)/(a × a).
229 := ((aa + aa − a) × aa/a − a − a)/a.
230 := ((aa + aa − a) × aa/a − a)/a.
231 := (aa + aa − a) × aa/(a × a).
232 := (aa × aa/a + aaa)/a.
233 := (aaa + aaa + aa)/a.
234 := (aaa + aaa + aa + a)/a.
235 := (aaa + aaa + aa + a + a)/a.
236 := (aaa + aaa + aa + a + a + a)/a.
237 := ((aaa + a + a) × (a + a)/a + aa)/a.
238 := (aa × aa/a − a − a) × (a + a)/(a × a).
239 := ((aa + aa) × aa/a − a − a − a)/a.
240 := ((aa + aa) × aa/a − a − a)/a.
241 := ((aa + aa) × aa/a − a)/a.
242 := (aa + aa) × aa/(a × a).
243 := ((aa + aa) × aa/a + a)/a.
244 := (aaa + aa) × (a + a)/(a × a).
245 := (aaa + aaa + aa + aa + a)/a.
246 := (aaa + aa + a) × (a + a)/(a × a).
247 := ((aaa + aa + a) × (a + a)/a + a)/a.
248 := (aaa + aa + a + a) × (a + a)/(a × a).
249 := ((aaa + aa + a + a) × (a + a)/a + a)/a.
250 := (aaaa − aaa)/(a + a + a + a).
251 := ((aa + aa + a) × aa/a − a − a)/a.
252 := ((aa + aa + a) × aa/a − a)/a.
253 := (aa + aa + a) × aa/(a × a).
254 := ((aa + aa + a) × aa/a + a)/a.
255 := ((aa + aa + a) × aa/a + a + a)/a.
256 := (aaa + aaa + aa + aa + aa + a)/a.
257 := (aaa + aaa + aa + aa + aa + a + a)/a.
258 := ((aaa + aa + a) × (a + a)/a + a + aa)/a.
259 := (aaa/(a + a + a) × aa + aaa)/(a + a).
260 := ((aa + aa) × (aa + a)/a − a − a − a − a)/a.
261 := ((aa + aa) × (aa + a)/a − a − a − a)/a.
262 := ((aa + aa) × (aa + a)/a − a − a)/a.
263 := ((aa + aa) × (aa + a)/a − a)/a.
264 := (aa + aa) × (aa + a)/(a × a).
265 := ((aa + aa) × (aa + a)/a + a)/a.
266 := (aaa + aa + aa) × (a + a)/(a × a).
267 := ((aaa + aa + aa) × (a + a)/a + a)/a.
268 := (aaa + aa + aa + a) × (a + a)/(a × a).
269 := ((aaa + aa + aa + a) × (a + a)/a + a)/a.
270 := (a − aaa + a + a) × (a − aa)/((a + a + a + a) × a).
271 := ((aa + aa) × aaa/(a + a + a) − a)/(a + a + a).
272 := (aaaa − aa − aa − a)/(a + a + a + a).
273 := (aa + aa − a) × (aa + a + a)/(a × a).
274 := (aaaa − aa − a − a − a − a)/(a + a + a + a).
275 := (aaaa − aa)/(a + a + a + a).
276 := (aa + aa + a) × (aa + a)/(a × a).
277 := ((aaaa − a)/(a + a) × a − a)/(a + a).
278 := (aaaa + a)/(a + a + a + a).
279 := (aaaa + a)/(a + a + a + a) + a/a.
280 := (aaa + a)/(a + a) × (aa − a)/(a + a).
281 := (aaaa + aa + a + a)/(a + a + a + a).
282 := (aaaa + aaa) × (a + a + a)/((aa + a + a) × a).
283 := (aaaa + aa + aa − a)/(a + a + a + a).
284 := ((aa + a + a) × (aa + aa)/a − a − a)/a.
285 := ((aa + a + a) × (aa + aa)/a − a)/a.
286 := (aa + aa) × (aa + a + a)/(a × a).
287 := ((aa + a + a) × (aa + aa)/a + a)/a.
288 := (aa + aa + a + a) × (aa + a)/(a × a).
289 := ((aa + aa + aa) × (aaa − aa)/aa − aa)/a.
290 := (aaa + aa + aa + aa + a) × (a + a)/(a × a).
291 := (aaaa × (a + a + a)/aa − aa − a)/a.
292 := (aaaa × (a + a + a)/aa − aa)/a.
293 := (aaaa × (a + a + a)/aa − aa + a)/a.
294 := (aaa − aa − a − a) × (a + a + a)/(a × a).
295 := (aaa/(a + a + a) × aa − aaa − a)/a.
296 := (aaa/(a + a + a) × aa − aaa)/a.
297 := (aaa − aa − a) × (a + a + a)/(a × a).
298 := ((aaa − aa) × (a + a + a)/a − a − a)/a.
299 := ((aaa − aa) × (a + a + a)/a − a)/a.
300 := (aaa − aa) × (a + a + a)/(a × a).
301 := ((aaa − aa) × (a + a + a)/a + a)/a.
302 := (aaaa × (a + a + a)/aa − a)/a.
303 := aaaa × (a + a + a)/(aa × a).
304 := (aaaa × (a + a + a)/aa + a)/a.
305 := (aaa × aa − a × a)/((a + a) × (a + a)).
306 := (aaaa + aa) × (a + a + a)/(aa × a).
307 := ((aaa + a)/(a + a) × aa − a − a)/(a + a).
308 := (aaa + a)/(a + a) × aa/(a + a).
309 := ((aaa + a)/(a + a) × aa + a + a)/(a + a).
310 := (aaa + aaa + aaa − aa − aa − a)/a.
311 := (aaa + aaa + aaa − aa − aa)/a.
312 := (aa + aa + a + a) × (aa + a + a)/(a × a).
313 := (aaaa/aa × (a + a) + aaa)/a.
314 := (aaaa × (a + a + a)/aa + aa)/a.
315 := ((aaaa + aa)/aa × (a + a) + aaa)/a.
316 := (aaa/(a + a + a) × aaa + a)/(aa + a + a).
317 := ((aaaa + aa) × (a + a + a)/aa + aa)/a.
318 := ((aaaa + aa) × (a + a + a)/aa + aa + a)/a.
319 := ((aaa + a)/(a + a) × aa + aa + aa)/(a + a).
320 := (aa + aa + aa − a) × (aa − a)/(a × a).
321 := (aaa + aaa + aaa − aa − a)/a.
322 := (aaa + aaa + aaa − aa)/a.
323 := (aaa × (a + a + a)/a − aa + a)/a.
324 := (aaa − a − a − a) × (a + a + a)/(a × a).
325 := ((aaa + a) × (a + a + a)/a − aa)/a.
326 := ((aaa − a − a) × (a + a + a)/a − a)/a.
327 := (aaa − a − a) × (a + a + a)/(a × a).
328 := ((aaa − a) × (a + a + a)/a − a − a)/a.
329 := ((aaa − a) × (a + a + a)/a − a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
330 := (aaa − a) × (a + a + a)/(a × a).
331 := (aaa + aaa + aaa − a − a)/a.
332 := (aaa + aaa + aaa − a)/a.
333 := aaa × (a + a + a)/(a × a).
334 := (aaa + aaa + aaa + a)/a.
335 := (aaa + aaa + aaa + a + a)/a.
336 := (aaa + a) × (a + a + a)/(a × a).
337 := (aaaa − aaa + aa)/(a + a + a).
338 := ((aaa + a) × (a + a + a)/a + a + a)/a.
339 := (aaa + a + a) × (a + a + a)/(a × a).
340 := (aa + aa + aa + a) × (aa − a)/(a × a).
341 := (aa + aa + aa − a − a) × aa/(a × a).
342 := (aaa + a + a + a) × (a + a + a)/(a × a).
343 := (aaa × (a + a) + aa × aa)/(a × a).
344 := (aaa + aaa + aaa + aa)/a.
345 := ((aaa + a) × (a + a) + aa × aa)/(a × a).
346 := (aaa + aaa + aaa + aa + a + a)/a.
347 := ((aaa + a) × (a + a + a)/a + aa)/a.
348 := ((aaa + a) × (a + a + a)/a + aa + a)/a.
349 := ((aaa + a) × (a + a + a)/a + aa + a + a)/a.
350 := ((aa + aa) × aa/a + aaa − a − a − a)/a.
351 := ((aa + aa) × aa/a + aaa − a − a)/a.
352 := (aa + aa + aa − a) × aa/(a × a).
353 := ((aa + aa) × aa/a + aaa)/a.
354 := (aaa + aaa + aaa + aa + aa − a)/a.
355 := (aaa + aaa + aaa + aa + aa)/a.
356 := (aaa − aa − aa) × (aa + a)/((a + a + a) × a).
357 := ((aaa − a) × (aa + a + a)/(a + a) − a)/(a + a).
358 := ((aaa − a) × aa/(a + a) + aaa)/(a + a).
359 := (aaaa − aa − aa − aa − a)/(a + a + a).
360 := (aaa + aa − a − a) × (a + a + a)/(a × a).
361 := ((aaa + aa − a − a) × (a + a + a)/a + a)/a.
362 := ((aa + aa + aa) × aa/a − a)/a.
363 := (aa + aa + aa) × aa/(a × a).
364 := ((aa + aa + aa) × aa/a + a)/a.
365 := ((aaa + aa) × (a + a + a)/a − a)/a.
366 := (aaa + aa) × (a + a + a)/(a × a).
367 := (aaaa − aa + a)/(a + a + a).
368 := (aaaa − a)/(a + a + a) − (a + a)/a.
369 := (aaaa − a)/(a + a + a) − a/a.
370 := (aaaa − a)/(a + a + a).
371 := (aaaa + a + a)/(a + a + a).
372 := (aaaa + a + a)/(a + a + a) + a/a.
373 := (aaaa + aa)/(a + a + a) − a/a.
374 := (aaaa + aa)/(a + a + a).
375 := (aaaa + aa)/(a + a + a) + a/a.
376 := (aaaa + aa)/(a + a + a) + (a + a)/a.
377 := (aaaa + aa + aa − a − a)/(a + a + a).
378 := (aaaa + aa + aa + a)/(a + a + a).
379 := (aaaa + a)/(a + a + a + a) + aaaa/aa.
380 := (aaa + a + a + a) × (aa − a)/((a + a + a) × a).
381 := (aaaa + aa + aa + aa − a)/(a + a + a).
382 := (aaaa/aa × (a + a) − aa) × (a + a)/(a × a).
383 := (aaaa − aaa − aaa − aaa − aa − a)/(a + a).
384 := (aa + aa + aa − a) × (aa + a)/(a × a).
385 := (aa + aa + aa + a + a) × aa/(a × a).
386 := (aa + aa + aa + a + a) × aa/(a × a) + a/a.
387 := (aa + aa + aa + a + a) × aa/(a × a) + (a + a)/a.
388 := (aaa − aa − a − a − a) × (aa + a)/((a + a + a) × a).
389 := (aaaa − aaa − aaa − aaa)/(a + a).
390 := (aaaa − aaa − aaa − aaa + a + a)/(a + a).
391 := ((aaa + aa) × aa/(a + a) + aaa)/(a + a).
392 := (aaa − aa − a − a) × (aa + a)/((a + a + a) × a).
393 := ((aa + aa + aa) × (aa + a)/a − a − a − a)/a.
5
394 := ((aa + aa + aa) × (aa + a)/a − a − a)/a.
395 := ((aa + aa + aa) × (aa + a)/a − a)/a.
396 := (aa + aa + aa) × (aa + a)/(a × a).
397 := ((aaa + aa) × (aa + a + a)/(a + a) + a)/(a + a).
398 := (aaa + aaa − aa − aa − a) × (a + a)/(a × a).
399 := (aaa + aa + aa) × (a + a + a)/(a × a).
400 := (aaa − aa) × (a + a + a + a)/(a × a).
401 := ((aaa − aa) × (a + a + a + a)/a + a)/a.
402 := (aaaa/aa × (a + a) − a) × (a + a)/(a × a).
403 := ((aaaa + aaaa) × (a + a)/aa − a)/a.
404 := aaaa × (a + a + a + a)/(aa × a).
405 := (aaa/(a + a + a) × aa − a − a)/a.
406 := (aaa/(a + a + a) × aa − a)/a.
407 := aaa/(a + a + a) × aa/a.
408 := (aaa/(a + a + a) × aa + a)/a.
409 := (aaa/(a + a + a) × aa + a + a)/a.
410 := (aaa/(a + a + a) × aa + a + a + a)/a.
411 := (aaaa + aaa + aa)/(a + a + a).
412 := (aaaa + aaa + aa + a + a + a)/(a + a + a).
413 := (aaaa × (a + a + a)/aa + aaa − a)/a.
414 := (aaaa × (a + a + a)/aa + aaa)/a.
415 := (aaaa × (a + a + a)/aa + aaa + a)/a.
416 := (aaa/(a + a + a) × aa + aa − a − a)/a.
417 := (aaa/(a + a + a) × aa + aa − a)/a.
418 := (aaa/(a + a + a) × aa + aa)/a.
419 := (aaa/(a + a + a) × aa + aa + a)/a.
420 := (aaa + aaa − aa − a) × (a + a)/(a × a).
421 := ((aaa + aaa − aa) × (aa + aa)/aa − a)/a.
422 := (aaa + aaa − aa) × (a + a)/(a × a).
423 := ((aaa + aaa − aa) × (aa + aa)/aa + a)/a.
424 := (aaaa/aa × (a + a) + aaa + aaa)/a.
425 := ((aa + aa + a) × aaa/(a + a + a) − a)/(a + a).
426 := ((aa + aa + a) × aaa/(a + a + a) + a)/(a + a).
427 := (aa + aa − a) × (aaa + aa)/((a + a) × (a + a + a)).
428 := (aaa − a − a − a − a) × (aa + a)/((a + a + a) × a).
429 := (aa + aa + aa) × (aa + a + a)/(a × a).
430 := ((aaa + aaa − a) × (aa + aa)/aa − aa − a)/a.
431 := ((aa + aa + a) × aaa/(a + a + a) + aa)/(a + a).
432 := (aaa − a − a − a) × (aa + a)/((a + a + a) × a).
433 := (aaa + aaa + aaa + aaa − aa)/a.
434 := (aaaa × (aa + a + a)/aa − aa)/(a + a + a).
435 := ((aaa − a − a) × (aa + a)/(a + a + a) − a)/a.
436 := (aaa − a − a) × (aa + a)/((a + a + a) × a).
437 := ((aaa − a − a) × (aa + a)/(a + a + a) + a)/a.
438 := (aaa + aaa − a − a − a) × (a + a)/(a × a).
439 := (aaaa − aaa − aaa − aa)/(a + a).
440 := (aaa − a) × (a + a + a + a)/(a × a).
441 := ((aaa − a) × (a + a + a + a)/a + a)/a.
442 := (aaa + aaa − a) × (a + a)/(a × a).
443 := (aaa + aaa + aaa + aaa − a)/a.
444 := (aaa + aaa) × (a + a)/(a × a).
445 := (aaaa − aaa − aaa + a)/(a + a).
446 := (aaa + aaa + a) × (a + a)/(a × a).
447 := ((aaa + a) × (a + a + a + a)/a − a)/a.
448 := (aaa + a) × (a + a + a + a)/(a × a).
449 := ((aaa + a) × (a + a + a + a)/a + a)/a.
450 := (aaaa − aaa − aaa + aa)/(a + a).
451 := (aaa + aa + a) × aa/((a + a + a) × a).
452 := (aaa + a + a) × (aa + a)/((a + a + a) × a).
453 := (aaaa × (aa − a − a)/aa − a − a − a)/(a + a).
454 := (aaa × (a + a + a) + aa × aa)/(a × a).
455 := ((a + a + a + a) × aaa/a + aa)/a.
456 := (aaa + a + a + a) × (aa + a)/((a + a + a) × a).
457 := (aaa × aaa/(aa − a − a) + a + a)/(a + a + a).
6
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
458 := ((aaa + aaa + a) × (aa + aa)/aa + aa + a)/a.
459 := (aaaa + aa) × (aa − a − a)/((a + a) × aa).
460 := (aaaa × (aa − a − a)/aa + aa)/(a + a).
461 := (aaaa + aa)/(a + a) − (aaaa − aa)/aa.
462 := (aa + aa − a) × (aa + aa)/(a × a).
463 := (aaaaa + a) × a/((aa + a) × (a + a)).
464 := (aaa + aaa + aa − a) × (a + a)/(a × a).
465 := (aaaa + aa + aa − a)/(a + a) − aaaa/aa.
466 := (aaa + aaa + aa) × (a + a)/(a × a).
467 := ((aaaa + aa) × (aa − a)/(aa + a) − a)/(a + a).
468 := (aaa + aaa + aa + a) × (a + a)/(a × a).
469 := (aaa/(a + a + a) × aa + aaaa − aaa)/(a + a + a).
470 := (aaa + aaa + aa + a + a) × (a + a)/(a × a).
471 := (aaaa − a)/(a + a + a) + aaaa/aa.
472 := ((aa + a + a + a) × aaaa/aa + a + a)/(a + a + a).
473 := ((aaaa + aa) × aa/(a + a) − aa − aa)/(aa + a + a).
474 := ((aaa + a)/(a + a) × (aaa − a) + a + a)/(aa + a + a).
475 := ((aa + a + a + a) × aaaa/aa + aa)/(a + a + a).
476 := (aaaa + aa) × (aa + a + a + a)/(aa × (a + a + a)).
477 := (aaaa + a + a) × (aa + a)/((a + a) × (aa + a + a + a)).
478 := ((aaa + a) × aaa/(a + a) − a − a)/(aa + a + a).
479 := ((aaa + a) × aaa/(a + a) + aa)/(aa + a + a).
480 := (aaaa/aa − (aa − a)/(a + a)) × (aa − a)/(a + a).
481 := (aa + a + a) × aaa/((a + a + a) × a).
482 := (aa + a + a) × aaa/((a + a + a) × a) + a/a.
483 := (aaaaa − a − a)/(aa + aa + a).
484 := (aa + aa) × (aa + aa)/(a × a).
485 := ((aa + aa) × (aa + aa)/a + a)/a.
486 := ((aa + aa) × (aa + aa)/a + a + a)/a.
487 := (aaaa × aaa/aa − aa + a)/(aa + aa + a).
488 := (aaa + aa) × (a + a + a + a)/(a × a).
489 := (aaaa − aaa − aa − aa)/(a + a).
490 := (aaaa − aaa)/(a + a) − (aaa − a)/aa.
491 := ((aaa + aa + a) × (aa + a)/(a + a + a) − a)/a.
492 := (aaa + aa + a) × (aa + a)/((a + a + a) × a).
493 := (aaaa − aaa − aa − a − a − a)/(a + a).
494 := (aaaa − aaa − aa − a)/(a + a).
495 := (aaaa − aaa − aa + a)/(a + a).
496 := (aaaa − aaa − aa + a + a + a)/(a + a).
497 := ((aaaa − aaa)/(a + a) × a − a − a − a)/a.
498 := ((aaaa − aaa)/(a + a) × a − a − a)/a.
499 := (aaaa − aaa − a − a)/(a + a).
500 := (aaaa − aaa)/(a + a).
501 := (aaaa − aaa + a + a)/(a + a).
502 := ((aaaa − aaa)/(a + a) × a + a + a)/a.
503 := ((aaa + a) × (aa − a − a)/(a + a) − a)/a.
504 := (aaa + a) × (aa − a − a)/((a + a) × a).
505 := (aaaaa − a)/(aa + aa).
506 := (aa + aa + a) × (aa + aa)/(a × a).
507 := (aaaa − aaa + aa + a + a + a)/(a + a).
508 := ((aaaa − a) × aa/(a + a) − aa + a + a)/(aa + a).
509 := ((aaa − aa) × (aaa + a)/(a + a) − a)/aa.
510 := (aaaa + aa)/aa × (aa − a)/(a + a).
511 := (aaaa − aaa + aa + aa)/(a + a).
512 := (aaaa − aaa + aa + aa + a + a)/(a + a).
513 := (aaaa − aa)/(a + a) − aaa/(a + a + a).
514 := ((aaa + a) × aaaa/(aa + aa) − a − a)/aa.
515 := ((aaa + a) × (aa − a − a)/(a + a) + aa)/a.
516 := ((aaa + a) × (aa − a − a)/(a + a) + aa + a)/a.
517 := ((aaa + a) × aaa/(aa + a) − a − a)/(a + a).
518 := (aaa/(a + a + a) × aa + aaa)/a.
519 := (aaa/(a + a + a) × aa + aaa + a)/a.
520 := (aaa/(a + a + a) × aa + aaa + a + a)/a.
521 := ((aaaa + aa)/(aa + aa) × (aa − a) + aa)/a.
522 := (aaaa − aa)/(a + a) − (aaa + a)/(a + a + a + a).
523 := (aaaa − (aa + a) × aa/(a + a) + a)/(a + a).
524 := (aaaa + aa)/(a + a) − aaa/(a + a + a).
525 := (aa + aa + a + a + a) × (aa + aa − a)/(a × a).
526 := ((aaaa + aaaa) × (a + a)/aa + aaa + aa)/a.
527 := (aaaa − a)/(a + a) − (aaa + a)/(a + a + a + a).
528 := (aa + aa + aa + aa) × (aa + a)/(a × a).
529 := (aa + aa + a) × (aa + aa + a)/(a × a).
530 := ((aaaaa − a − a)/(aa + aa − a) × a + a)/a.
531 := ((aaa + aa + aa) × (aa + a)/(a + a + a) − a)/a.
532 := (aaa + aa + aa) × (aa + a)/((a + a + a) × a).
533 := (aaa + aa + a) × (aa + a + a)/((a + a + a) × a).
534 := (aaaa − aa − aa − aa − aa + a)/(a + a).
535 := (aaa − a − a − a − a) × (aaa − a)/((aa + aa) × a).
536 := (aaa + aa + aa + a) × (aa + a)/((a + a + a) × a).
537 := (aaaa − aaa)/(a + a) + aaa/(a + a + a).
538 := (aaaa − aa − aa − aa − a − a)/(a + a).
539 := (aaaa − aa − aa − aa)/(a + a).
540 := (aaaa − aa − aa − aa + a + a)/(a + a).
541 := ((aaaa − aa)/(aa + aa) × aa − aa + a + a)/a.
542 := aaaaa × (aa + a)/((aaa + aa + a) × (a + a)).
543 := (aaaa − aa − aa − a − a − a)/(a + a).
544 := (aaaa − a)/(a + a) − aa/a.
545 := (aaaa + a)/(a + a) − aa/a.
546 := (aaaa − aa − aa + a + a + a)/(a + a).
547 := (aaaa + a)/(a + a) + a/a − (aaa − a)/aa.
548 := (aaaa − aa − a − a − a − a)/(a + a).
549 := (aaaa − aa − a − a)/(a + a).
550 := (aaaa − aa)/(a + a).
551 := (aaaa − aa + a + a)/(a + a).
552 := ((aaaa − aa)/(a + a) × a + a + a)/a.
553 := (aaaa − a)/(a + a) − (a + a)/a.
554 := (aaaa − a − a − a)/(a + a).
555 := (aaaa − a)/(a + a).
556 := (aaaa + a)/(a + a).
557 := (aaaa + a + a + a)/(a + a).
558 := (aaaa + a)/(a + a) + (a + a)/a.
559 := ((aaa + a) × (aa − a)/(a + a) − a)/a.
560 := (aaaa + aa − a − a)/(a + a).
561 := (aaaa + aa)/(a + a).
562 := (aaaa + aa + a + a)/(a + a).
563 := (aaaa + aa + a + a + a + a)/(a + a).
564 := ((aaa + a) × aaa/(a + a) − aa − a)/aa.
565 := (aaa + a + a) × (aa − a)/((a + a) × a).
566 := (aaaa − a)/(a + a) + aa/a.
567 := (aaaa + a)/(a + a) + aa/a.
568 := (aaaa + aa + aa + a + a + a)/(a + a).
569 := ((aaaa + a) × aa/(aa + aa) + aa + a + a)/a.
570 := (aaa + a + a + a) × (aaa − a)/((aa + aa) × a).
571 := (aaaa + aa + aa + aa − a − a)/(a + a).
572 := (aaaa + aa + aa + aa)/(a + a).
573 := (aaaa + aa + aa + aa + a + a)/(a + a).
574 := (aaa + aa + a) × (aaa + a)/((aa + a) × (a + a)).
575 := (aaa − aa) × (aa + aa + a)/((a + a + a + a) × a).
576 := (aaa + aa + aa + aa) × (aa + a)/((a + a + a) × a).
577 := (aaaa + aa + aa + aa + aa − a)/(a + a).
578 := (aaaa + aa + aa + aa + aa + a)/(a + a).
579 := (aaaaa − aaa + a)/(aa + aa − a − a − a).
580 := ((aaa + a) × aaa/(aa + aa − a) − aa − a)/a.
581 := ((aaa + a) × aaa/(aa + aa − a) − aa)/a.
582 := (aaaaa + aaaa)/(aa + aa − a).
583 := (aaa + a)/(a + a + a + a) + (aaaa − a)/(a + a).
584 := (aaa + a)/(a + a + a + a) + (aaaa + a)/(a + a).
585 := (aaa + aaa + aa + a)/(a + a) × (aa − a)/(a + a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
586 := ((aa + aa + a) × aa + aaa × (a + a + a))/(a × a).
587 := (aaaa − aa)/(a + a) + aaa/(a + a + a).
588 := (aa + aa − a) × (aaa + a)/((a + a + a + a) × a).
589 := ((aaa − aa) × (aa + a)/(a + a) − aa)/a.
590 := ((aaa − aa) × (aa + a)/(a + a) − aa + a)/a.
591 := ((aaa + a) × aaa/(aa + aa − a) − a)/a.
592 := (aaa + a) × aaa/(aa + aa − a)/a.
593 := ((aaa − a) × aa/(a + a) − aa − a)/a.
594 := ((aaa − a) × aa/(a + a) − aa)/a.
595 := (aaaa × (aa + a)/(aa + aa) − aa)/a.
596 := (aaaa × (aa + a)/(aa + aa) − aa + a)/a.
597 := ((aaa − aa) × (aa + a)/(a + a) − a − a − a)/a.
598 := ((aaa − aa) × (aa + a)/(a + a) − a − a)/a.
599 := ((aaa − a − a) × aa/a − a)/(a + a).
600 := (aaa − aa) × (aa + a)/((a + a) × a).
601 := ((aaa − aa) × (aa + a)/(a + a) + a)/a.
602 := ((aaa − a) × aa/(a + a) − a − a − a)/a.
603 := ((aaa − a) × aa/(a + a) − a − a)/a.
604 := ((aaa − a) × aa/(a + a) − a)/a.
605 := (aaa − a) × aa/((a + a) × a).
606 := ((aaa − a) × aa/(a + a) + a)/a.
607 := ((aaa − a) × aa/(a + a) + a + a)/a.
608 := (aaaa × (aa + a)/(aa + aa) + a + a)/a.
609 := ((aaa × aa − a × a)/(a + a) − a)/a.
610 := ((aaa × aa)/a − a)/(a + a).
611 := (aaaa + aaa)/(a + a).
612 := (aaaa + aaa + a + a)/(a + a).
613 := (aaaa + aaa + a + a + a + a)/(a + a).
614 := ((aaa + a)/(a + a) × aa − a − a)/a.
615 := ((aaa + a)/(a + a) × aa − a)/a.
616 := (aaa + a)/(a + a) × aa/a.
617 := ((aaa + a)/(a + a) × aa + a)/a.
618 := ((aaa + a)/(a + a) × aa + a + a)/a.
619 := ((aaa + a)/(a + a) × aa + a + a + a)/a.
620 := ((aaa + aa) × (aaa + a)/(a + a) − aa − a)/aa.
621 := ((aaa + a + a) × aa/a − a)/(a + a).
622 := ((aaa + a + a) × aa/a + a)/(a + a).
623 := (aaaa + aaa + aa + aa + a + a)/(a + a).
624 := ((aaa + a)/(a + a) × aa + aa − a − a − a)/a.
625 := ((aaa + a)/(a + a) × aa + aa − a − a)/a.
626 := ((aaa + a)/(a + a) × aa + aa − a)/a.
627 := ((aaa + a)/(a + a) × aa + aa)/a.
628 := ((aaa + a)/(a + a) × aa + aa + a)/a.
629 := ((aaa + a)/(a + a) × aa + aa + a + a)/a.
630 := (aaa + aaa − aa − a) × (a + a + a)/(a × a).
631 := aaaaaa/aaa − (aaaa − a)/(a + a + a).
632 := (aaa + aaa − aa) × (a + a + a)/(a × a) − a/a.
633 := (aaa + aaa − aa) × (a + a + a)/(a × a).
634 := (aaa + aaa − aa) × (a + a + a)/(a × a) + a/a.
635 := (aaa + aaa)/(a + a + a) + (aaaa + aa)/(a + a).
636 := (aaaa+a+a)×(aa−a−a−a)/((aa+a+a+a)×a).
637 := aaaaaa × (aa + a + a + a)/(aa + aa)/aaa.
638 := ((aaa + a)/(a + a) × aa + aa + aa)/a.
639 := (aaaa + aaa)/(a + a) + (aaa + a)/(a + a + a + a).
640 := ((aa + aa − a) × (aaa + aa)/(a + a) − a)/(a + a).
641 := ((aaa + aaa + aaa − aa − a) × (a + a)/a − a)/a.
642 := (aaa + aaa + aaa − aa − a) × (a + a)/(a × a).
643 := ((aaa − a − a) × (aa + a)/(a + a) − aa)/a.
644 := (aaa × (aa + a)/(a + a) − aa − aa)/a.
645 := (aaaa − aa − aa − a)/(a + a) + aaaa/aa.
646 := (aaaa − aa − aa + a)/(a + a) + aaaa/aa.
647 := ((aaaa + a) × (aa + a + a)/(a + a) − aaa)/aa.
648 := (aaaa + aaa)/(a + a) + aaa/(a + a + a).
649 := ((aaaa − aa) × (aa + a + a)/(a + a) − aa)/aa.
7
650 := (aaa − aa) × (aa + a + a)/((a + a) × a).
651 := ((aaa − aa) × (aa + a + a)/(a + a) + a)/a.
652 := (aaaa + aa)/aa + (aaaa − aa)/(a + a).
653 := ((aaa − a − a) × (aa + a)/(a + a) − a)/a.
654 := (aaa − a − a) × (aa + a)/((a + a) × a).
655 := (aaa × (aa + a)/(a + a) − aa)/a.
656 := (aaa × (aa + a)/(a + a) − aa + a)/a.
657 := (aaa × (aa + a)/(a + a) − aa + a + a)/a.
658 := ((aaa + aa) × aa/(a + a) − aa − a − a)/a.
659 := ((aaa − a) × (aa + a)/(a + a) − a)/a.
660 := (aaa − a) × (aa + a)/((a + a) × a).
661 := ((aaa − a) × (aa + a)/(a + a) + a)/a.
662 := (aaaa + aa)/(a + a) + aaaa/aa.
663 := (aaa + aaa − a) × (a + a + a)/(a × a).
664 := (aaa × (aa + a)/(a + a) − a − a)/a.
665 := (aaa × (aa + a)/(a + a) − a)/a.
666 := aaa × (aa + a)/((a + a) × a).
667 := (aaa × (aa + a)/(a + a) + a)/a.
668 := (aaa × (aa + a)/(a + a) + a + a)/a.
669 := (aaa + aaa + a) × (a + a + a)/(a × a).
670 := ((aaa + aa) × aa/(a + a) − a)/a.
671 := (aaa + aa) × aa/((a + a) × a).
672 := (aaa + a) × (aa + a)/((a + a) × a).
673 := ((aaa + a) × (aa + a)/(a + a) + a)/a.
674 := ((aaa + a) × (aa + a)/(a + a) + a + a)/a.
675 := ((aaa + a) × (aa + a)/(a + a) + a + a + a)/a.
676 := ((aaa + aa) × aaa/(a + a) − aa)/(aa − a).
677 := (aaa × (aa + a)/(a + a) + aa)/a.
678 := (aaa + a + a) × (aa + a)/((a + a) × a).
679 := ((aaa + a + a) × (aa + a)/(a + a) + a)/a.
680 := (aaa × aaa/(aa − a − a) − aa + a + a)/(a + a).
681 := ((aaa + aa) × aa/(a + a) + aa − a)/a.
682 := ((aaa + aa) × aa/(a + a) + aa)/a.
683 := ((aaa + aa) × aa/(a + a) + aa + a)/a.
684 := (aaa × aaa/(aa − a − a) − a)/(a + a).
685 := (aaa × aaa/(aa − a − a) + a)/(a + a).
686 := (aaa + aaa + aaa + aa − a) × (a + a)/(a × a).
687 := ((aaaa + aa) × aa/(a + a) + aa + a)/(aa − a − a).
688 := (aaa + aaa + aaa + aa) × (a + a)/(a × a).
689 := ((aaa + a + a) × (aa + a)/(a + a) + aa)/a.
690 := (aaa × aaa/(aa − a − a) + aa)/(a + a).
691 := ((aaa + a) × aaa/(a + a) + a + a + a)/(aa − a − a).
692 := (aaaa − aaa/(a + a + a) × aa − aa − a)/a.
693 := (aa + aa + aa) × (aa + aa − a)/(a × a).
694 := (aaaa + a)/(aa − a − a − a) + (aaaa − a)/(a + a).
695 := ((aaaaa + a)/(aa − a − a − a) × a + a)/(a + a).
696 := (aaa + aaa + aa − a) × (a + a + a)/(a × a).
697 := ((aaa + a) × (aaa + a)/(a + a) + a)/(aa − a − a).
698 := ((aaaa + aa) × aa/(a + a) + aaa)/(aa − a − a).
699 := (aaa + aaa + aa) × (a + a + a)/(a × a).
700 := (aa + aa − a) × (aaa − aa)/((a + a + a) × a).
701 := ((aaa + aa) × (aa + aa + a)/(a + a) − a)/(a + a).
702 := (aaa + aaa + aa + a) × (a + a + a)/(a × a).
703 := (aaaa − aaa/(a + a + a) × aa − a)/a.
704 := (aaaa − aaa/(a + a + a) × aa)/a.
705 := (aaaa − aaa/(a + a + a) × aa + a)/a.
706 := (aaaa × (aa + a)/(aa + aa) + aaa − aa)/a.
707 := (aa + a + a + a) × aaaa/(aa × (a + a)).
708 := ((aa + a + a + a) × aaaa/aa + a + a)/(a + a).
709 := ((aaa − aa) × (aa + a)/(a + a) + aaa − a − a)/a.
710 := ((aaa − aa) × (aa + a)/(a + a) + aaa − a)/a.
711 := ((aaa − aa) × (aa + a)/(a + a) + aaa)/a.
712 := (aaa − aa − aa) × (aa − a − a − a)/(a × a).
713 := ((aa + a + a + a) × aaaa/aa + aa + a)/(a + a).
8
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
714 := ((aaa − a) × (aa + a + a)/(a + a) − a)/a.
715 := (aaa − a) × (aa + a + a)/((a + a) × a).
716 := ((aaa − a) × aa/(a + a) + aaa)/a.
717 := ((aaa − a) × aa/(a + a) + aaa + a)/a.
718 := ((aaa − a) × aa/(a + a) + aaa + a + a)/a.
719 := ((aaa − a) × aa/(a + a) + aaa + a + a + a)/a.
720 := ((aa + a + a) × aaa/a − a − a − a)/(a + a).
721 := ((aa + a + a) × aaa/a − a)/(a + a).
722 := ((aa + a + a) × aaa/a + a)/(a + a).
723 := ((aa + a + a) × aaa/a + a + a + a)/(a + a).
724 := ((aa + a) × aa × aa/((a + a) × a) − a − a)/a.
725 := ((aa + a) × aa × aa/((a + a) × a) − a)/a.
726 := (aa + a) × aa × aa/((a + a) × a × a).
727 := ((aaa − a) × aa/(a + a) + aaa + aa)/a.
728 := (aaa + a) × (aa + a + a)/((a + a) × a).
729 := (aaa + a) × (aa + a + a)/((a + a) × a) + a/a.
730 := ((aaa + aa) × (aa + a)/(a + a) − a − a)/a.
731 := ((aaa + aa) × (aa + a)/(a + a) − a)/a.
732 := (aaa + aa) × (aa + a)/((a + a) × a).
733 := ((aaa + aa) × (aa + a)/(a + a) + a)/a.
734 := ((aaa + aa) × (aa + a)/(a + a) + a + a)/a.
735 := ((aaa + aa) × (aa + a)/(a + a) + a + a + a)/a.
736 := (aaaa + aaaa − aa − a − a − a)/(a + a + a).
737 := (aaaa + aaaa − aa)/(a + a + a).
738 := ((aaaa − a)/(a + a + a) × (a + a) − a − a)/a.
739 := ((aaaa − a)/(a + a + a) × (a + a) − a)/a.
740 := (aaaa − a) × (a + a)/((a + a + a) × a).
741 := ((aaaa − a)/(a + a + a) × (a + a) + a)/a.
742 := (aaaa + a + a) × (a + a)/((a + a + a) × a).
743 := ((aaa + aa) × (aa + a)/(a + a) + aa)/a.
744 := (aaaa + aaaa + aa − a)/(a + a + a).
745 := (aaaa + aaaa + aa + a + a)/(a + a + a).
746 := (aaaa + aaaa + a)/(a + a + a) + (aa − a)/(a + a).
747 := ((aaaa + aaa)/(a + a) × aa + a + a)/(aa − a − a).
748 := (aaaa + aa) × (a + a)/((a + a + a) × a).
749 := ((aaaa + aa + a) × (aa + aa)/aa + a)/(a + a + a).
750 := (aaaa − aaa) × (a + a + a)/((a + a) × (a + a)).
751 := (aaaaaa × (a + a + a)/aaa + a)/(a + a + a + a).
752 := ((aa + a + a + a + a) × aaaa/aa − aa)/(a + a).
753 := (aaaa × (aa + a)/(a + a) + aaa)/(aa − a − a).
754 := (aaaa + aa + aa − a − a) × (a + a)/((a + a + a) × a).
755 := ((aaa − aa)/(a + a) + aaaa/aa) × (aa − a)/(a + a).
756 := ((aa − a − a − a) × aaa − (aa + a) × aa)/(a × a).
757 := ((aa − a − a) × aaa − (aa + aa) × aa)/(a × a).
758 := ((aa + a + a + a + a) × aaaa/aa + a)/(a + a).
759 := (aa + aa + aa) × (aa + aa + a)/(a × a).
760 := (aaa/(a + a + a) × aa + aaaa + a + a)/(a + a).
761 := ((aaa + aa) × aa/(a + a) + aaa − aa − aa + a)/a.
762 := ((aaaa−a)×aa/(a+a)−aa+a+a)/(aa−a−a−a).
763 := (aa + aa − a) × (aaa − a − a)/((a + a + a) × a).
764 := ((aaa − a − a) × (aa + a)/(a + a) + aaa − a)/a.
765 := ((aaa − a − a) × (aa + a)/(a + a) + aaa)/a.
766 := (aaaa − aaa − aaa − aaa − aa − a)/a.
767 := (aaaa − aaa − aaa − aaa − aa)/a.
768 := (aaaa − aaa − aaa − aaa − aa + a)/a.
769 := (aaaaa − aaaa − a − a − a)/(aa + a + a).
770 := (aa + aa − a) × (aaa − a)/((a + a + a) × a).
771 := ((aaa + aa) × aa/(a + a) + aaa − aa)/a.
772 := ((aaa + aa) × aa/(a + a) + aaa − aa + a)/a.
773 := ((aaa + aa) × aa/(a + a) + aaa − aa + a + a)/a.
774 := (aaaa + aaaa + aaa − aa)/(a + a + a).
775 := (aaaa − aaa − aaa − aaa − a − a − a)/a.
776 := (aaaa − aaa − aaa − aaa − a − a)/a.
777 := (aa − a − a − a − a) × aaa/(a × a).
778 := (aaaa − aaa − aaa − aaa)/a.
779 := (aaaa − aaa − aaa − aaa + a)/a.
780 := (aaa − aa − aa − aa) × (aa − a)/(a × a).
781 := (aaaa + aaaa + aaa + aa − a)/(a + a + a).
782 := ((aaa + aa) × aa/(a + a) + aaa)/a.
783 := ((aaa + a) × (aa + a)/(a + a) + aaa)/a.
784 := (aa + aa − a) × (aaa + a)/((a + a + a) × a).
785 := (aaaaa − aaa − aa + a)/(aa + a + a + a).
786 := ((aa − a − a − a) × aaaa/aa − aa − aa)/a.
787 := (aaaa − aaa − aaa − aaa + aa − a − a)/a.
788 := (aaaa − aaa − aaa − aaa + aa − a)/a.
789 := (aaaa − aaa − aaa − aaa + aa)/a.
790 := (aaaa − aaa − aaa − aaa + aa + a)/a.
791 := (aaa + a + a) × (aa + aa − a)/((a + a + a) × a).
792 := (aa + a) × (aa + a) × aa/((a + a) × a × a).
793 := (aaa + aa) × (aa + a + a)/((a + a) × a).
794 := ((aaa + aa) × (aa + a + a)/(a + a) + a)/a.
795 := (aaaa + a + a) × (aa − a)/((aa + a + a + a) × a).
796 := ((aa − a − a − a) × aaaa/aa − aa − a)/a.
797 := ((aa − a − a − a) × aaaa/aa − aa)/a.
798 := (aaa + aa + aa) × (aa + a)/((a + a) × a).
799 := (aaaa × (aa − a − a)/aa − aaa + a)/a.
800 := (aa − aaa) × (a − aa + a + a)/(a × a).
801 := (aaa − aa − aa) × (aa − a − a)/(a × a).
802 := ((aa + aa) × aaa/(a + a + a) − aa − a)/a.
803 := ((aa + aa) × aaa/(a + a + a) − aa)/a.
804 := ((aa + aa) × aaa/(a + a + a) − aa + a)/a.
805 := ((aa − a − a − a) × aaaa/aa − a − a − a)/a.
806 := ((aa − a − a − a) × aaaa/aa − a − a)/a.
807 := ((aa − a − a − a) × aaaa/aa − a)/a.
808 := (aa − a − a − a) × aaaa/(aa × a).
809 := ((aa − a − a − a) × aaaa/aa + a)/a.
810 := ((aa − a − a − a) × aaaa/aa + a + a)/a.
811 := ((aa + aa) × aaa/(a + a + a) − a − a − a)/a.
812 := ((aa + aa) × aaa/(a + a + a) − a − a)/a.
813 := ((aa + aa) × aaa/(a + a + a) − a)/a.
814 := (aa + aa) × aaa/(a + a + a)/a.
815 := ((aa + aa) × aaa/(a + a + a) + a)/a.
816 := (aaa/(a + a + a) × aa + a) × (a + a)/(a × a).
817 := (aaaaaa + a)/(aaa + aa + aa + a + a + a).
818 := (aaa/(a + a + a) × aa + a + a) × (a + a)/(a × a).
819 := ((aa − a − a − a) × aaaa/aa + aa)/a.
820 := ((aa − a − a − a) × aaaa/aa + aa + a)/a.
821 := ((aa − a − a − a) × aaaa/aa + aa + a + a)/a.
822 := (aaaa + aaa + aa) × (a + a)/((a + a + a) × a).
823 := ((aaaaa + a)/(a + a + a) × (a + a) − a)/(aa − a − a).
824 := ((aaaa + aa) × (aa − a)/(aa + a) − aaa)/a.
825 := (aaaa − aa) × (a + a + a)/((a + a) × (a + a)).
826 := (aaaaa + a)/(aa + a) − (aaaa − aa)/aa.
827 := ((aaa − a) × aa/(a + a) + aaa + aaa)/a.
828 := ((aaa − a) × aa/(a + a) + aaa + aaa + a)/a.
829 := ((aa − a − a − a) × aaaa/aa + aa + aa − a)/a.
830 := ((aa + a) × (aa + a)/(a + a) + aa) × (aa − a)/(a × a).
831 := (a − aaaa + a + a) × (a − aa + a)/((aa + a) × a).
832 := (aaaa × (aa + a)/(a + a) − aa + a)/(aa − a − a − a).
833 := (aaaaa − aaaa − a − a − a − a)/(aa + a).
834 := (aaaa + a) × (a + a + a)/(a + a)/(a + a).
835 := (aaa − aaaa − a − a) × (a − aa)/((aa + a) × a).
836 := (aaa + a + a + a) × (aa + aa)/((a + a + a) × a).
837 := ((aaa − a) × aa/(a + a) + aaa + aaa + aa − a)/a.
838 := ((aaa − a) × aa/(a + a) + aaa + aaa + aa)/a.
839 := ((aaa + a) × (aa + a + a)/(a + a) + aaa)/a.
840 := (aaa + aaa − aa − a) × (aa + a)/((a + a + a) × a).
841 := ((aaaa + aa) × (a + a + a)/(a + a) − a)/(a + a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
842 := ((aaa + aa) × (aa + a)/(a + a) + aaa − a)/a.
843 := ((aaa + aa) × (aa + a)/(a + a) + aaa)/a.
844 := (aaa + aaa − aa) × (aa + a)/((a + a + a) × a).
845 := ((aaa + aa) × aaa/(a + a) − aa)/(aa − a − a − a).
846 := (aaaaa − aaa − a − a)/(aa + a + a).
847 := (aaaaa − aaa + aa)/(aa + a + a).
848 := ((aaaaa − aa)/(aa + a) × aa + a)/(aa + a).
849 := ((aaaaa + a)/(aa + a) × aa + a + a)/(aa + a).
850 := ((aa + aa + a) × aaa/(a + a + a) − a)/a.
851 := (aa + aa + a) × aaa/((a + a + a) × a).
852 := ((aa + aa + a) × aaa/(a + a + a) + a)/a.
853 := (aaaaa − aa − aa)/(aa + a + a).
854 := (aaaaa − aa + a + a)/(aa + a + a).
855 := (aaaaa + a + a + a + a)/(aa + a + a).
856 := (aaaa − aaa − aaa − aa − aa − aa)/a.
857 := ((aaa − a) × aa/(a + a) + aaaa − a − a)/(a + a).
858 := (aaa − aa − aa − aa) × aa/(a × a).
859 := ((aaa − a) × aa/(a + a) + aaaa + a + a)/(a + a).
860 := (aaa − aa − aa − a − a − a) × (aaa − a)/(aa × a).
861 := (aaa + aa + a) × (aa + aa − a)/((a + a + a) × a).
862 := ((aa + aa + a) × aaa/(a + a + a) + aa)/a.
863 := ((aaa + a)/(a + a) × aa + aaaa − a)/(a + a).
864 := (aa + a) × (aa + a) × (aa + a)/((a + a) × a × a).
865 := (aaaaa + a)/(aa + a) − (aaa + aa)/(a + a).
866 := (aaaa − aaa − aaa − aa − aa − a)/a.
867 := (aaaa − aaa − aaa − aa − aa)/a.
868 := (aaa + aa + a + a) × (aa + aa − a)/((a + a + a) × a).
869 := (aaaaa − aa)/(aa + a) − (aaa + a)/(a + a).
870 := (aaaaa + a)/(aa + a) − (aaa + a)/(a + a).
871 := (aaaaa + a)/(aa + a) − (aaa − a)/(a + a).
872 := (a − aa + a + a) × (a − aaa + a)/(a × a).
873 := (aaaaa + aaaa)/(aa + a + a + a).
874 := (aaaa − aaa − aaa − aa − a − a − a − a)/a.
875 := (aaaa − aaa − aaa − aa − a − a − a)/a.
876 := (aaaa − aaa − aaa − aa − a − a)/a.
877 := (aaaa − aaa − aaa − aa − a)/a.
878 := (aaaa − aaa − aaa − aa)/a.
879 := (aaaa − aaa − aaa − aa + a)/a.
880 := (a − aa + a + a) × (a − aaa)/(a × a).
881 := ((a − aa + a + a) × (a − aaa)/a + a)/a.
882 := (aaa − aa − a − a) × (aa − a − a)/(a × a).
883 := (aaa × (aa + a)/(a + a) + aaaa − aa)/(a + a).
884 := (aaa + aaa − a) × (aa + a)/((a + a + a) × a).
885 := (aaaa − aaa − aaa − a − a − a − a)/a.
886 := (aaaa − aaa − aaa − a − a − a)/a.
887 := (aaaa − aaa − aaa − a − a)/a.
888 := (aa − a − a − a) × aaa/(a × a).
889 := (aaaa − aaa − aaa)/a.
890 := (aaaa − aaa − aaa + a)/a.
891 := (aaaa − aaa − aaa + a + a)/a.
892 := (aaaa − aaa − aaa + a + a + a)/a.
893 := (aaaa − aaa − aaa + a + a + a + a)/a.
894 := (aaa × (aa + a)/(a + a) + aaaa + aa)/(a + a).
895 := (aaaa − aaa − aaa)/a + (aa + a)/(a + a).
896 := (aa − a − a − a) × (aaa + a)/(a × a).
897 := (aaaaa − aaaa − aaa − aa − aa)/aa.
898 := (aaaaa − aaaa − aaa − aa)/aa.
899 := (aaaaa − aaaa − aaa)/aa.
900 := (aa − aaa) × (a − aa + a)/(a × a).
901 := (aaaa − aaa − aaa + aa + a)/a.
902 := (aaa + aa + a) × (aa + aa)/((a + a + a) × a).
903 := (aaaa − aaa − aaa + aa + a + a + a)/a.
904 := (aaa + a + a) × (aa − a − a − a)/(a × a).
905 := (aaaa − (aaaa + aa + aa) × (a + a)/aa)/a.
9
906 := (aaaa × (aa − a − a)/aa − a − a − a)/a.
907 := (aaaa × (aa − a − a)/aa − a − a)/a.
908 := (aaaa × (aa − a − a)/aa − a)/a.
909 := aaaa × (aa − a − a)/aa/a.
910 := (aaaa × (aa − a − a)/aa + a)/a.
911 := (aaaa − aaa − aaa + aa + aa)/a.
912 := (aaa + a + a + a) × (aa − a − a − a)/(a × a).
913 := (aaa + aaa + aaa − a) × aa/(a + a)/(a + a).
914 := ((aaa + a) × aaa/(aa + a) − aaa − aa)/a.
915 := (aaaaa − aa)/(aa + a) − (aaa − a)/aa.
916 := ((aaaa + aaa) × (a + a + a)/(a + a) − a)/(a + a).
917 := ((aaaa + aaa) × (a + a + a)/(a + a) + a)/(a + a).
918 := (aaaa + aa) × (aa − a − a)/(aa × a).
919 := (aaaa × (aa − a − a)/aa + aa − a)/a.
920 := (aaaa × (aa − a − a)/aa + aa)/a.
921 := (aaaa × (aa − a − a)/aa + aa + a)/a.
922 := (aaaa × (aa − a − a)/aa + aa + a + a)/a.
923 := (aaaaa − aa − aa − aa − a − a)/(aa + a).
924 := (aaaaa − aa − aa − a)/(aa + a).
925 := (aaaaa − aa)/(aa + a).
926 := (aaaaa + a)/(aa + a).
927 := (aaaaa + a)/(aa + a) + a/a.
928 := (aaaaa + aa + aa + a + a + a)/(aa + a).
929 := ((aaaa + aa) × (aa − a − a)/aa + aa)/a.
930 := (aaaaa − aa)/(aa + a) + (aa − a)/(a + a).
931 := (aaaaa + a)/(aa + a) + (aa − a)/(a + a).
932 := (aaaaa + a)/(aa + a) + (aa + a)/(a + a).
933 := ((aa − aaa + aa) × (aa + aa)/aa + aaaa)/a.
934 := ((aaaa + aa) × (aa − a)/(aa + a) − a)/a.
935 := (aaaa + aa) × (aa − a)/(aa + a)/a.
936 := (aaaaa + aaa + aa − a)/(aa + a).
937 := (aaaaa + aaa + aa + aa)/(aa + a).
938 := (aaa + aa + aa + a) × (aa + aa − a)/((a + a + a) × a).
939 := (aaaaa + aa + aa + a + a + a)/(aa + a) + aa/a.
940 := (aaaa + aaa)/(aa + a + a) × (aa − a)/a.
941 := (aaaaa + aaaa + aa)/(aa + a + a).
942 := ((aaaa − a) × (aaa + a)/(aa + a) + a + a)/aa.
943 := (aaa + aa + a) × (aa + aa + a)/((a + a + a) × a).
944 := ((aaaaa − aaa) × (a + a)/aa − aaa − a)/(a + a).
945 := aaaaaa/aaa − (aaa + a)/(a + a).
946 := (aaa − aa − aa − a − a − a) × aa/(a × a).
947 := ((aaa + a) × aaa − aa × aa)/((aa + a + a) × a).
948 := ((aaa + aa) × aaaa/aa + a + a)/(aa + a + a).
949 := (aaaaa − a)/aa − (aaa + aa)/(a + a).
950 := (aaa + a + a + a) × (aaa − aa)/((aa + a) × a).
951 := ((aaa + a + a) × aaaa/aa − a)/(aa + a).
952 := (aa + aa + aa + a) × (aaa + a)/(a + a)/(a + a).
953 := (aaaaa − aa − a)/aa − (aaa + a)/(a + a).
954 := (aaaaa − a)/aa − (aaa + a)/(a + a).
955 := (aaaaa − a)/aa − (aaa − a)/(a + a).
956 := (aaaa − aaa − aa − aa − aa − aa)/a.
957 := (aaa − aa − aa − a − a) × aa/(a × a).
958 := (aaa − aa − aa − a − a) × aa/(a × a) + a/a.
959 := ((aa + aa − a − a − a) × aaaa/aa − a)/(a + a).
960 := (aaa − aa − a − a − a − a) × (aa − a)/(a × a).
961 := (aaaaaa/(aa + aa − a) × (a + a) − aa)/aa.
962 := (aaa + aaa) × (aa + a + a)/((a + a + a) × a).
963 := (aaa − a − a − a − a) × (aa − a − a)/(a × a).
964 := aaaaaa/aaa − aaa/(a + a + a).
965 := (aaaa − aaa − aa − aa − aa − a − a)/a.
966 := (aaaa − aaa − aa − aa − aa − a)/a.
967 := (aaaa − aaa − aa − aa − aa)/a.
968 := (aaa − aa − aa − a) × aa/(a × a).
969 := (aaa + a + a + a) × (aaaa + aa)/aa/(aa + a).
10
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
970 := (aaa − aa − a − a − a) × (aaa − a)/(aa × a).
971 := (aaaaa + aaaaa + aaa)/(aa + aa + a).
972 := (a − aaa + a + a) × (a − aa + a)/(a × a).
973 := (aaaaa − a)/aa − aaa/(a + a + a).
974 := (aaaaa − a)/aa − aaa/(a + a + a) + a/a.
975 := (aaaa − aaa − aa − aa − a − a − a)/a.
976 := (aaa + aa) × (aa − a − a − a)/(a × a).
977 := (aaaa − aaa − aa − aa − a)/a.
978 := (aaaa − aaa − aa − aa)/a.
979 := (aaa − aa − aa) × aa/(a × a).
980 := (aaa − aa − a − a) × (aaa − a)/(aa × a).
981 := (a − aaa + a) × (a − aa + a)/(a × a).
982 := (a − aaa + a) × (a − aa + a)/(a × a) + a/a.
983 := (a − aaa + a) × (a − aa + a)/(a × a) + (a + a)/a.
984 := (aaa + aa + a) × (aa − a − a − a)/(a × a).
985 := (aaaa − aaa − aa − a − a − a − a)/a.
986 := (aaaa − aaa − aa − a − a − a)/a.
987 := (aaaa − aaa − aa − a − a)/a.
988 := (aaaa − aaa − aa − a)/a.
989 := (aaaa − aaa − aa)/a.
990 := (aaaa − aaa − aa + a)/a.
991 := (aaaa − aaa − aa + a + a)/a.
992 := (aaaa − aaa − aa + a + a + a)/a.
993 := (aaaa − aaa − aa + a + a + a + a)/a.
994 := (aaaa − aaa)/a − (aa + a)/(a + a).
995 := (aaaa − aaa − a − a − a − a − a)/a.
996 := (aaaa − aaa − a − a − a − a)/a.
997 := (aaaa − aaa − a − a − a)/a.
998 := (aaaa − aaa − a − a)/a.
999 := (aaaa − aaa − a)/a.
1000 := (aaaa − aaa)/a.
1001 := (aaaa − aaa + a)/a.
1002 := (aaaa − aaa + a + a)/a.
1003 := (aaaa − aaa + a + a + a)/a.
1004 := (aaaa − aaa + a + a + a + a)/a.
1005 := (aaaaa − a)/aa − (aa − a)/(a + a).
1006 := aaaaaa/aaa + (aa − a)/(a + a).
1007 := (aaaaa − aa − aa − aa − a)/aa.
1008 := (aaa + a) × (aa − a − a)/(a × a).
1009 := (aaaaa − aa − a)/aa.
1010 := (aaaaa − a)/aa.
1011 := (aaaa − aaa + aa)/a.
1012 := (aaaa − aaa + aa + a)/a.
1013 := (aaaa − aaa + aa + a + a)/a.
1014 := (aaaa − aaa + aa + a + a + a)/a.
1015 := (aaaaa − a)/aa + (aa − a)/(a + a).
1016 := (aaaaa − a)/aa + (aa + a)/(a + a).
1017 := (aaa + a + a) × (aa − a − a)/(a × a).
1018 := ((aaa + a + a) × (aa − a − a)/a + a)/a.
1019 := ((aaa + a + a) × (aa − a − a)/a + a + a)/a.
1020 := (aaaaa + aaa − a − a)/aa.
1021 := (aaaa − aaa + aa + aa − a)/a.
1022 := (aaaa − aaa + aa + aa)/a.
1023 := (aaaa − aaa + aa + aa + a)/a.
1024 := (aaaa − aaa + aa + aa + a + a)/a.
1025 := ((aaa + a) × aaa/(aa + a) − aa)/a.
1026 := (aaa + a + a + a) × (aa − a − a)/(a × a).
1027 := (aaa/(a + a + a) × aaa + a)/(a + a + a + a).
1028 := ((aaaa + aa) × (aa + aa)/(aa + a) − a)/(a + a).
1029 := ((aaaa + aa + aa) × (aa − a)/aa − a)/a.
1030 := (aaaa + aa + aa) × (aa − a)/(aa × a).
1031 := (aaaa − aaa + aa + aa + aa − a − a)/a.
1032 := (aaaa − aaa + aa + aa + aa − a)/a.
1033 := (aaaa − aaa + aa + aa + aa)/a.
1034 := ((aaa + a) × aaa/(aa + a) − a − a)/a.
1035 := ((aaa + a) × aaa/(aa + a) − a)/a.
1036 := (aaa + a) × aaa/((aa + a) × a).
1037 := ((aaa + a) × aaa/(aa + a) + a)/a.
1038 := ((aaa + a) × aaa/(aa + a) + a + a)/a.
1039 := (aaaa − (aa + a) × (aa + a)/(a + a))/a.
1040 := (aaaa + aa + aa + aa) × (aa − a)/(aa × a).
1041 := ((aaaa + aa + aa) × (aa − a)/aa + aa)/a.
1042 := (aaaa − aaa + aa + aa + aa + aa − a − a)/a.
1043 := (aaaa − aaa + aa + aa + aa + aa − a)/a.
1044 := (aaaa − aaa + aa + aa + aa + aa)/a.
1045 := (aaaa − (aa + a) × aa/(a + a))/a.
1046 := (aaaa − (aa + a) × aa/(a + a) + a)/a.
1047 := ((aaa + a) × aaa/(aa + a) + aa)/a.
1048 := ((aaa + a) × aaa/(aa + a) + aa + a)/a.
1049 := (aaaa + aaaa − aaa − aa − a − a)/(a + a).
1050 := (aaaa + aaaa − aaa − aa)/(a + a).
1051 := aaaaaa/aaa + (aaa − aa)/(a + a).
1052 := aaaaaa/aaa + (aaa − aa)/(a + a) + a/a.
1053 := ((aaaa − a) × aaa/(aa − a − a) − a)/(aa + a + a).
1054 := (aaaa + aaaa − aaa − a − a − a)/(a + a).
1055 := (aaaa + aaaa − aaa − a)/(a + a).
1056 := (aaaa + aaaa − aaa + a)/(a + a).
1057 := aaaaaa/aaa + (aaa + a)/(a + a).
1058 := ((aaa + a) × aaa/(aa + a) + aa + aa)/a.
1059 := (aaaaa − aa − a)/aa + (aaa − aa)/(a + a).
1060 := (aaaaa − a)/aa + (aaa − aa)/(a + a).
1061 := (aaaa + aaaa − aaa + aa)/(a + a).
1062 := aaaaaa/aaa + (aaa + aa)/(a + a).
1063 := (aaaaa − aaa)/(aa − a) − aaa/(a + a + a).
1064 := (aaa + a + a + a) × (aaa + a)/((aa + a) × a).
1065 := (aaaaa − a)/aa + (aaa − a)/(a + a).
1066 := (aaaa − aa − aa − aa − aa − a)/a.
1067 := (aaaa − aa − aa − aa − aa)/a.
1068 := (aaa − aa − aa) × (aa + a)/(a × a).
1069 := (aaaa − aa − aa − aa − aa + a + a)/a.
1070 := (aaa − a − a − a − a) × (aa − a)/(a × a).
1071 := (aaaa + aa) × (aa + aa − a)/(aa × (a + a)).
1072 := (aaaa − aaa × aa/(aa + aa + aa) − a − a)/a.
1073 := (aaaa − aaa × aa/(aa + aa + aa) − a)/a.
1074 := (aaaa − aaa × aa/(aa + aa + aa))/a.
1075 := (aaaa − aa − aa − aa − a − a − a)/a.
1076 := (aaaa − aa − aa − aa − a − a)/a.
1077 := (aaaa − aa − aa − aa − a)/a.
1078 := (aaaa − aa − aa − aa)/a.
1079 := (aaaa − aa − aa − aa + a)/a.
1080 := (aaa − a − a − a) × (aa − a)/(a × a).
1081 := (aaaa − aa − aa − aa + a + a + a)/a.
1082 := (aaaa − aa − aa − aa + a + a + a + a)/a.
1083 := (aaaaa × (aa + a)/(aaa + aa + a) − a)/a.
1084 := aaaaa × (aa + a)/(aaa + aa + a)/a.
1085 := (aaaaa × (aa + a)/(aaa + aa + a) + a)/a.
1086 := (aaaa − aa − aa − a − a − a)/a.
1087 := (aaaa − aa − aa − a − a)/a.
1088 := (aaaa − aa − aa − a)/a.
1089 := (aaaa − aa − aa)/a.
1090 := (aaaa − aa − aa + a)/a.
1091 := (aaaa − aa − aa + a + a)/a.
1092 := (aaaa − aa − aa + a + a + a)/a.
1093 := (aaaa − aa − aa + a + a + a + a)/a.
1094 := (aaaa − aa − a − a − a − a − a − a)/a.
1095 := (aaaa − aa − a − a − a − a − a)/a.
1096 := (aaaa − aa − a − a − a − a)/a.
1097 := (aaaa − aa − a − a − a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1098 := (aaaa − aa − a − a)/a.
1099 := (aaaa − aa − a)/a.
1100 := (aaaa − aa)/a.
1101 := (aaaa − aa + a)/a.
1102 := (aaaa − aa + a + a)/a.
1103 := (aaaa − aa + a + a + a)/a.
1104 := (aaaa − aa + a + a + a + a)/a.
1105 := (aaaa − a − a − a − a − a − a)/a.
1106 := (aaaa − a − a − a − a − a)/a.
1107 := (aaaa − a − a − a − a)/a.
1108 := (aaaa − a − a − a)/a.
1109 := (aaaa − a − a)/a.
1110 := (aaaa − a)/a.
1111 := aaaa/a.
1112 := (aaaa + a)/a.
1113 := (aaaa + a + a)/a.
1114 := (aaaa + a + a + a)/a.
1115 := (aaaa + a + a + a + a)/a.
1116 := (aaaa + aaaa + aa − a)/(a + a).
1117 := (aaaa + aaaa + aa + a)/(a + a).
1118 := (aaaa + aa − a − a − a − a)/a.
1119 := (aaaa + aa − a − a − a)/a.
1120 := (aaaa + aa − a − a)/a.
1121 := (aaaa + aa − a)/a.
1122 := (aaaa + aa)/a.
1123 := (aaaa + aa + a)/a.
1124 := (aaaa + aa + a + a)/a.
1125 := (aaaa + aa + a + a + a)/a.
1126 := (aaaa + aa + a + a + a + a)/a.
1127 := (aaaa + aa + a + a + a + a + a)/a.
1128 := (aaaa + aa)/a + (aa + a)/(a + a).
1129 := (aaaa + aa + a)/a + (aa + a)/(a + a).
1130 := (aaa + a + a) × (aa − a)/(a × a).
1131 := (aaaa + aa + aa − a − a)/a.
1132 := (aaaa + aa + aa − a)/a.
1133 := (aaaa + aa + aa)/a.
1134 := (aaaa + aa + aa + a)/a.
1135 := (aaaa + aa + aa + a + a)/a.
1136 := (aaaa + aa + aa + a + a + a)/a.
1137 := (aaaa + aa + aa + a + a + a + a)/a.
1138 := (aaaa + aa + aa)/a + (aa − a)/(a + a).
1139 := (aaaa + aa + aa)/a + (aa + a)/(a + a).
1140 := (aaa + a + a + a) × (aa − a)/(a × a).
1141 := (aaaa + aa + aa + aa − a − a − a)/a.
1142 := (aaaa + aa + aa + aa − a − a)/a.
1143 := (aaaa + aa + aa + aa − a)/a.
1144 := (aaaa + aa + aa + aa)/a.
1145 := (aaaa + aa + aa + aa + a)/a.
1146 := (aaaa + aa + aa + aa + a + a)/a.
1147 := ((aaa + a) × aaa/(aa + a) + aaa)/a.
1148 := (aaa + aa + a) × (aaa + a)/(aa + a)/a.
1149 := ((aaa + a) × aaa/(aa + a) + aaa + a + a)/a.
1150 := (aaa + a + a + a + a) × (aa − a)/(a × a).
1151 := (aaaa + aa + aa + aa + aa − a − a − a − a)/a.
1152 := (aaaa + aa + aa + aa + aa − a − a − a)/a.
1153 := (aaaa + aa + aa + aa + aa − a − a)/a.
1154 := (aaaa + aa + aa + aa + aa − a)/a.
1155 := (aaaa + aa + aa + aa + aa)/a.
1156 := (aaaa + aa + aa + aa + aa + a)/a.
1157 := (aaaa + aa + aa + aa + aa + a + a)/a.
1158 := ((aaa + a) × aaa/(aa + a) + aaa + aa)/a.
1159 := (aaa + a + a + a) × (aaa + aa)/((aa + a) × a).
1160 := (aaaaa − (aaa + aa) × aa/(a + a))/(aa − a − a).
1161 := (aaaa + aaaa + aaa − aa)/(a + a).
11
1162 := ((aa + aa + a) × aaaa/aa + a)/(a + a).
1163 := (aaa − aa − a − a − a) × (aa + a)/(a × a) − a/a.
1164 := (aaa − aa − a − a − a) × (aa + a)/(a × a).
1165 := (aaaa + aa + aa + aa + aa + aa − a)/a.
1166 := (aaaa + aaaa + aaa − a)/(a + a).
1167 := (aaaa + aaaa + aaa + a)/(a + a).
1168 := (aaaa + aaaa + aaa + a + a + a)/(a + a).
1169 := (aaaa−aaa+a+a)×(aa+a+a+a)/((aa+a)×a).
1170 := (aaa + aaa + aa + a) × (aaa − a)/((a + a) × aa).
1171 := (aaaa + aaaa + aaa + aa − a − a)/(a + a).
1172 := (aaaa + aaaa + aaa + aa)/(a + a).
1173 := (aaaa + aa) × (aa + aa + a)/((a + a) × aa).
1174 := ((aaaa + aa) × (aa + aa + a)/(a + a) + aa)/aa.
1175 := (aaa × aa − (aa + aa + a) × (a + a))/(a × a).
1176 := (aaa − aa − a − a) × (aa + a)/(a × a).
1177 := (aaa − a − a − a − a) × aa/(a × a).
1178 := (aaaa + aaa − aa − aa − aa − aa)/a.
1179 := ((a − aa − aa) × (a + a) + aaa × aa)/(a × a).
1180 := (aaa+aa−a−a−a−a)×(aaa−aa)/((aa−a)×a).
1181 := (aaa − a − a − a − a) × (aa − a)/(a × a) + aaa/a.
1182 := (aaa × aa − (aa + a + a) × (a + a + a))/(a × a).
1183 := aaaaaa × (aa + a + a)/(aaa × aa).
1184 := (aa + aa + aa − a) × aaa/((a + a + a) × a).
1185 := (aaa × aa − (a + a + a) × (aa + a))/(a × a).
1186 := (aaaa + aaa − aa − aa − aa − a − a − a)/a.
1187 := (aaaa + aaa − aa − aa − aa − a − a)/a.
1188 := (aaa − a − a − a) × aa/(a × a).
1189 := (aaaa + aaa − aa − aa − aa)/a.
1190 := (aaaa × (aa + a)/aa − aa − aa)/a.
1191 := ((a − aa) × (a + a + a) + aaa × aa)/(a × a).
1192 := (aaaa × (aa + a) − (aaa − a) × (a + a))/(aa × a).
1193 := (aaaaaa × (aa + a)/aaa + aaaa)/aa.
1194 := (aa + a) × (aaa + aaa − aa − aa − a)/(a × (a + a)).
1195 := (aaa × aa − (aa + a + a) × (a + a))/(a × a).
1196 := (aaaa − aaa + aa + a) × (aa + a + a)/(aa × a).
1197 := (aaaa + aaa − aa − aa − a − a − a)/a.
1198 := (aaaa + aaa − aa − aa − a − a)/a.
1199 := (aaa − a − a) × aa/(a × a).
1200 := (aaa − aa) × (aa + a)/(a × a).
1201 := (aaaa × (aa + a)/aa − aa)/a.
1202 := (aaaa × (aa + a)/aa − aa + a)/a.
1203 := (aaaa × (aa + a)/aa − aa + a + a)/a.
1204 := (aaaa × (aa + a)/aa − aa + a + a + a)/a.
1205 := ((aa + aa) × aa/a − a) × (aa − a)/(a × (a + a)).
1206 := (aaa + aa + aa + a) × (aa − a − a)/(a × a).
1207 := (aaaa + aaa − aa − a − a − a − a)/a.
1208 := (aaaa + aaa − aa − a − a − a)/a.
1209 := (aaaa + aaa − aa − a − a)/a.
1210 := (aaa − a) × aa/(a × a).
1211 := (aaaa + aaa − aa)/a.
1212 := aaaa × (aa + a)/aa/a.
1213 := (aaaa × (aa + a)/aa + a)/a.
1214 := (aaaa × (aa + a)/aa + a + a)/a.
1215 := (aaaa × (aa + a)/aa + a + a + a)/a.
1216 := (aaaa + aaa)/a − (aa + a)/(a + a).
1217 := (aaaa + aaa)/a − (aa − a)/(a + a).
1218 := (aaaa + aaa − a − a − a − a)/a.
1219 := (aaaa + aaa − a − a − a)/a.
1220 := (aaaa + aaa − a − a)/a.
1221 := aaa × aa/(a × a).
1222 := (aaaa + aaa)/a.
1223 := (aaaa + aaa + a)/a.
1224 := (aaaa + aaa + a + a)/a.
1225 := (aaaa + aaa + a + a + a)/a.
12
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1226 := (aaaa + aaa + a + a + a + a)/a.
1227 := aaa × aa/(a × a) + (aa + a)/(a + a).
1228 := (aaaa + aaa)/a + (aa + a)/(a + a).
1229 := (aaaa + aaa + aa − a − a − a − a)/a.
1230 := (aaa + aa + a) × (aaa − a)/(aa × a).
1231 := (aaaa + aaa + aa − a − a)/a.
1232 := (aaa + a) × aa/(a × a).
1233 := (aaaa + aaa + aa)/a.
1234 := (aaaa + aaa + aa + a)/a.
1235 := (aaaa + aaa + aa + a + a)/a.
1236 := (aaaa + aaa + aa + a + a + a)/a.
1237 := (aaaaa + aa + aa)/(aa − a − a).
1238 := (aaaaa + aa + aa + aa − a − a)/(aa − a − a).
1239 := ((aaa − a − a) × (aa + a) + aaa × aaa)/(aa × a).
1240 := (aaa + aa + a + a) × (aa − a)/(a × a).
1241 := ((aaa + a + a) × aa/a − a − a)/a.
1242 := ((aaa + a + a) × aa/a − a)/a.
1243 := (aaa + a + a) × aa/(a × a).
1244 := (aaaa + aaa + aa + aa)/a.
1245 := (aaaa + aaa + aa + aa + a)/a.
1246 := (aaaa + aaa + aa + aa + a + a)/a.
1247 := ((aa + a + a) × (a + a) + aaa × aa)/(a × a).
1248 := (aaaaa + aaa + aa − a)/(aa − a − a).
1249 := ((aaa + aa + a + a + a) × (aa − a)/a − a)/a.
1250 := (aaa + aa + a + a + a) × (aa − a)/(a × a).
1251 := ((a + a + a) × (aa − a) + aaa × aa)/(a × a).
1252 := ((aaa + a + a + a) × aa/a − a − a)/a.
1253 := ((aaa + a + a + a) × aa/a − a)/a.
1254 := (aaa + a + a + a) × aa/(a × a).
1255 := (aaaa + aaa + aa + aa + aa)/a.
1256 := (aaaa + aaa + aa + aa + aa + a)/a.
1257 := ((a + a + a) × (aa + a) + aaa × aa)/(a × a).
1258 := (aaa × aaa/(aa − a − a) − aaa)/a.
1259 := (aaa × aaa/(aa − a − a) − aaa + a)/a.
1260 := (aaa × aaa/(aa − a − a) − aaa + a + a)/a.
1261 := (aaa × aaa/(aa − a − a) − aaa + a + a + a)/a.
1262 := ((a + a + a) × (aa − a) + (aaa + a) × aa)/(a × a).
1263 := ((aa + aa − a) × (a + a) + aaa × aa)/(a × a).
1264 := (aaaaa − aaaa + aaa + a)/(aa − a − a − a).
1265 := (aaa + a + a + a + a) × aa/(a × a).
1266 := (aaaa + aaa + aa + aa + aa + aa)/a.
1267 := (aaaa + aaa + aa + aa + aa + aa + a)/a.
1268 := ((aaa + a + a) × aaaa/aa − a)/(aa − a − a).
1269 := (aaa × aaa/(aa − a − a) − aaa + aa)/a.
1270 := (aaa × aaa/(aa − a − a) − aaa + aa + a)/a.
1271 := (aaa + aa + a + a) × (aaa + aa + a)/((aa + a) × a).
1272 := ((aaaaa − aa)/(aa + a) × aa + a)/(aa − a − a − a).
1273 := (aaaaaa × (aa + a + a + a)/aaa − aa)/aa.
1274 := (aaa − aa − a − a) × (aa + a + a)/(a × a).
1275 := (aaaaaa × (aa + a + a + a)/aaa + aa)/aa.
1276 := (aaa+aaa+aa−a)×(aa+aa)/((a+a+a+a)×a).
1277 := (aaaaaa − aa − a)/(aaa − aa − aa − a − a).
1278 := ((aa + aa − a) × (aaa + aa)/(a + a) − a − a − a)/a.
1279 := (aaaa + a)/(a + a + a + a) + aaaaaa/aaa.
1280 := ((aa + aa − a) × (aaa + aa)/(a + a) − a)/a.
1281 := (aa + aa − a) × (aaa + aa)/((a + a) × a).
1982 := ((aa + aa − a) × (aaa + aa)/(a + a) + a)/a.
1283 := ((aaaaa+a)×(a+a+a)/(a+a)+aa)/(aa+a+a).
1284 := (aaa − a − a − a − a) × (aa + a)/(a × a).
1985 := (aaa − a − a − a − a) × (aa + a)/(a × a) + a/a.
1286 := ((aaaa+a)×aaa/(aa+a)+a+a)/(aa−a−a−a).
1287 := (aaaa − aa − aa) × (aa + a + a)/(aa × a).
1288 := (aaa + a + a + a + a) × (aaa + a)/((aa − a) × a).
1289 := ((aaaa − aa) × (aa + a + a) − aa × aa)/(aa × a).
1990 := (aaaa/aa × (a + a) + aaaa − aa − aa − a)/a.
1291 := (aaaa/aa × (a + a) + aaaa − aa − aa)/a.
1292 := (aa+aa+aa+a)×(aaa+a+a+a)/((a+a+a)×a).
1293 := ((aaaa − aaa + a)/aa × (a + a) + aaaa)/a.
1994 := ((aaaa − aaa + a)/aa × (a + a) + aaaa + a)/a.
1295 := (aaaa − a) × (aa + a + a + a)/((aa + a) × a).
1296 := (aaa − a − a − a) × (aa + a)/(a × a).
1297 := ((aaa − a − a − a) × (aa + a)/a + a)/a.
1298 := ((aaa − a − a − a) × (aa + a)/a + a + a)/a.
1299 := ((aaa − aa) × (aa + a + a)/a − a)/a.
1300 := (aaa − aa) × (aa + a + a)/(a × a).
1301 := ((aaaa − aa) × (aa + a + a)/aa + a)/a.
1302 := (aaaa × (aa + a + a)/aa − aa)/a.
1303 := (aaaa × (aa + a + a)/aa − aa + a)/a.
1304 := ((aaaa + aa)/aa × (a + a) + aaaa − aa)/a.
1305 := ((aaa − a − a) × (aa + a)/a − a − a − a)/a.
1306 := ((aaa − a − a) × (aa + a)/a − a − a)/a.
1307 := ((aaa − a − a) × (aa + a)/a − a)/a.
1308 := (aaa − a − a) × (aa + a)/(a × a).
1309 := ((aaa − a − a) × (aa + a)/a + a)/a.
1310 := (aaaa + aaa + aaa − aa − aa − a)/a.
1311 := (aaaa + aaa + aaa − aa − aa)/a.
1312 := (aaaa × (aa + a + a)/aa − a)/a.
1313 := aaaa × (aa + a + a)/(aa × a).
1314 := (aaaa × (aa + a + a)/aa + a)/a.
1315 := (aaaa × (aa + a + a)/aa + a + a)/a.
1316 := ((aaaa + aa)/aa × (a + a) + aaaa + a)/a.
1317 := ((aaaa + aa + aa) × (a + a)/aa + aaaa)/a.
1318 := ((aaaa − aa) × (aa + a)/(aa − a) − a − a)/a.
1319 := ((aaaa − aa) × (aa + a)/(aa − a) − a)/a.
1320 := (aaaa − aa) × (aa + a)/((aa − a) × a).
1321 := (aaaa + aaa + aaa − aa − a)/a.
1322 := (aaaa + aaa + aaa − aa)/a.
1323 := (aaaa + aaa + aaa − aa + a)/a.
1324 := (aaaa + aaa + aaa − aa + a + a)/a.
1325 := ((aaaa + aa) × (aa + a + a)/aa − a)/a.
1326 := (aaaa + aa) × (aa + a + a)/(aa × a).
1327 := ((aaaa + aa) × (aa + a + a)/aa + a)/a.
1328 := ((aaa + aa − a) × aa/a − a − a − a)/a.
1329 := ((aaa + aa − a) × aa/a − a − a)/a.
1330 := ((aaa + aa − a) × aa/a − a)/a.
1331 := (aaa + aa − a) × aa/(a × a).
1332 := aaa × (aa + a)/(a × a).
1333 := (aaaa + aaa + aaa)/a.
1334 := (aaaa + aaa + aaa + a)/a.
1335 := (aaaa + aaa + aaa + a + a)/a.
1336 := (aaaa + aaa + aaa + a + a + a)/a.
1337 := (aaaa + aaa + aaa + a + a + a + a)/a.
1338 := ((aaa + aa) × aa/a − a − a − a − a)/a.
1339 := ((aaa + aa) × aa/a − a − a − a)/a.
1340 := ((aaa + aa) × aa/a − a − a)/a.
1341 := ((aaa + aa) × aa/a − a)/a.
1342 := (aaa + aa) × aa/(a × a).
1343 := ((aaa + aa) × aa/a + a)/a.
1344 := (aaa + a) × (aa + a)/(a × a).
1345 := (aaaa + aaa + aaa + aa + a)/a.
1346 := (aaaa + aaa + aaa + aa + a + a)/a.
1347 := (aaa × aaa/(aa − a − a) − aa − aa)/a.
1348 := (aaa × aaa/(aa − a − a) − aa − aa + a)/a.
1349 := ((aaa + aa + a) × aa/a − a − a − a − a)/a.
1350 := ((aaa + aa + a) × aa/a − a − a − a)/a.
1351 := ((aaa + aa + a) × aa/a − a − a)/a.
1352 := ((aaa + aa + a) × aa/a − a)/a.
1353 := (aaa + aa + a) × aa/(a × a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1354 := ((aaa + aa + a) × aa/a + a)/a.
1355 := ((aaa + aa + a) × aa/a + a + a)/a.
1356 := (aaa + a + a) × (aa + a)/(a × a).
1357 := ((aaa + a + a) × (aa + a)/a − a)/a.
1358 := (aaa × aaa/(aa − a − a) − aa)/a.
1359 := (aaa × aaa/(aa − a − a) − aa + a)/a.
1360 := (aaa × aaa/(aa − a − a) − aa + a + a)/a.
1361 := ((aaa + aa + a + a) × aa/a − a − a − a)/a.
1362 := ((aaa + aa + a + a) × aa/a − a − a)/a.
1363 := ((aaa + aa + a + a) × aa/a − a)/a.
1364 := (aaa + aa + a + a) × aa/(a × a).
1365 := ((aaa + aa + a + a) × aa/a + a)/a.
1366 := ((aaa + aa + a + a) × aa/a + a + a)/a.
1367 := ((aaa + a + a + a) × (aa + a)/a − a)/a.
1368 := (aaa + a + a + a) × (aa + a)/(a × a).
1369 := aaa × aaa/(aa − a − a)/a.
1370 := (aaa × aaa/(aa − a − a) + a)/a.
1371 := (aaa × aaa/(aa − a − a) + a + a)/a.
1372 := (aaa − aa − a − a) × (aa + a + a + a)/(a × a).
1373 := ((aaa + aa + a + a + a) × aa/a − a − a)/a.
1374 := ((aaa + aa + a + a + a) × aa/a − a)/a.
1375 := (aaa + aa + a + a + a) × aa/(a × a).
1376 := ((aaa + aa + a + a + a) × aa/a + a)/a.
1377 := ((aaa + aa + a + a + a) × aa/a + a + a)/a.
1378 := ((aaa + aa + a + a + a) × aa/a + a + a + a)/a.
1379 := (aaa × aaa/(aa − a − a) + aa − a)/a.
1380 := (aaa + a + a + a + a) × (aa + a)/(a × a).
1381 := (aaa × aaa/(aa − a − a) + aa + a)/a.
1382 := (aaa × aaa/(aa − a − a) + aa + a + a)/a.
1383 := (aaaaa + a)/(aa − a − a − a) − (aa + a)/(a + a).
1384 := (aaaaa + a)/(aa − a − a − a) − (aa − a)/(a + a).
1385 := ((aaa + a) × aaa/(a + a + a) + aa)/(a + a + a).
1386 := (aaa + aa + a + a + a + a) × aa/(a × a).
1387 := (aaaaa + a)/(aa − a − a − a) − (a + a)/a.
1388 := (aaaaa + a)/(aa − a − a − a) − a/a.
1389 := (aaaaa + a)/(aa − a − a − a).
1390 := (aaaaa + a)/(aa − a − a − a) + a/a.
1391 := (aaa − a − a − a − a) × (aa + a + a)/(a × a).
1392 := (aaaaa + aa + aa + a + a + a)/(aa − a − a − a).
1393 := (aaaaa + aa + aa + aa)/(aa − a − a − a).
1394 := ((aaa + a + a) × aaa/(a + a + a) + a)/(a + a + a).
1395 := (aaaaa + a)/(aa − a − a − a) + (aa + a)/(a + a).
1396 := ((aa + a + a + a) × (aaa − aa)/a − a − a − a − a)/a.
1397 := ((aa+a)×aa/(a+a)+aaaaa−a)/(aa−a−a−a).
1398 := (aaa + aaa + aa) × (aa + a) × aa/(a + a)/(aa × a).
1399 := ((aaa − aa − aa) × (a + a) + aaa × aa)/(a × a).
1400 := (aa + a + a + a) × (aaa − aa)/(a × a).
1401 := ((aa + a + a + a) × (aaa − aa)/a + a)/a.
1402 := ((aaa + aa) × (aa + aa + a)/(a + a) − a)/a.
1403 := (aaa + aa) × (aa + aa + a)/(a + a)/a.
1404 := (aaa − a − a − a) × (aa + a + a)/(a × a).
1405 := ((aaa − a − a − a) × (aa + a + a)/a + a)/a.
1406 := (aaa/(a + a + a) × aaa + aaa)/(a + a + a).
1407 := (aaa/(a + a + a) × aa + aaaa − aaa)/a.
1408 := (aaa/(a + a + a) × aa + aaaa − aaa + a)/a.
1409 := ((aa + a + a + a) × aaaa/aa − a − a − a − a − a)/a.
1410 := ((aa + a + a + a) × aaaa/aa − a − a − a − a)/a.
1411 := ((aa + a + a + a) × aaaa/aa − a − a − a)/a.
1412 := ((aa + a + a + a) × aaaa/aa − a − a)/a.
1413 := ((aa + a + a + a) × aaaa/aa − a)/a.
1414 := (aa + a + a + a) × aaaa/(aa × a).
1415 := ((aa + a + a + a) × aaaa/aa + a)/a.
1416 := ((aa + a + a + a) × aaaa/aa + a + a)/a.
1417 := (aaa − a − a) × (aa + a + a)/(a × a).
13
1418 := ((aaa − a − a) × (aa + a + a)/a + a)/a.
1419 := ((aaa − a − a) × (aa + a + a)/a + a + a)/a.
1420 := ((aaa − a − a) × (aa + a + a)/a + a + a + a)/a.
1421 := ((aaa − aa) × (a + a) + aaa × aa)/(a × a).
1422 := (aaaa + aaa + aaa + aaa − aa − aa)/a.
1423 := (aaaa × (aa + a + a)/aa + aaa − a)/a.
1424 := (aaaa × (aa + a + a)/aa + aaa)/a.
1425 := ((aa + a + a + a) × aaaa/aa + aa)/a.
1426 := ((aa + a + a + a) × aaaa/aa + aa + a)/a.
1427 := ((aaaa + aa) × (aa + a + a + a)/aa − a)/a.
1428 := (aaaa + aa) × (aa + a + a + a)/(aa × a).
1429 := ((aaa − a) × (aa + a + a)/a − a)/a.
1430 := (aaa − a) × (aa + a + a)/(a × a).
1431 := ((aaa − a) × (aa + a + a)/a + a)/a.
1432 := ((aaa − a) × (aa + a + a)/a + a + a)/a.
1433 := ((aaa − a) × (aa + a + a)/a + a + a + a)/a.
1434 := ((aaa − a) × (aa + a + a)/a + a + a + a + a)/a.
1435 := ((aaa − a) × (aa + a + a)/a + a + a + a + a + a)/a.
1436 := ((aaaa + aa) × (aa + a + a)/aa + aaa − a)/a.
1437 := ((aaaa + aa) × (aa + a + a)/aa + aaa)/a.
1438 := ((aaaa + aa) × (aa + a + a)/aa + aaa + a)/a.
1439 := ((aa + a + a) × aaa/a − a − a − a − a)/a.
1440 := ((aa + a + a) × aaa/a − a − a − a)/a.
1441 := ((aa + a + a) × aaa/a − a − a)/a.
1442 := ((aa + a + a) × aaa/a − a)/a.
1443 := (aa + a + a) × aaa/(a × a).
1444 := (aaaa + aaa + aaa + aaa)/a.
1445 := (aaaa + aaa + aaa + aaa + a)/a.
1446 := (aaaa + aaa + aaa + aaa + a + a)/a.
1447 := (aaaa + aaa + aaa + aaa + a + a + a)/a.
1448 := ((aaa + aa + aa − a) × aa/a − a − a − a − a)/a.
1449 := ((aaa + aa + aa − a) × aa/a − a − a − a)/a.
1450 := ((aaa + aa + aa − a) × aa/a − a − a)/a.
1451 := ((aaa + aa + aa − a) × aa/a − a)/a.
1452 := (aaa + aa + aa − a) × aa/(a × a).
1453 := ((aaa + aa + aa − a) × aa/a + a)/a.
1454 := (aaaa + aaa + aaa + aaa + aa − a)/a.
1455 := (aaaa + aaa + aaa + aaa + aa)/a.
1456 := (aaa + a) × (aa + a + a)/(a × a).
1457 := ((aaa + a) × (aa + a + a)/a + a)/a.
1458 := ((aaa + a) × (aa + a + a)/a + a + a)/a.
1459 := ((aaa + a) × (aa + a + a)/a + a + a + a)/a.
1460 := ((aaa + aa + aa) × aa/a − a − a − a)/a.
1461 := ((aaa + aa + aa) × aa/a − a − a)/a.
1462 := ((aaa + aa + aa) × aa/a − a)/a.
1463 := (aaa + aa + aa) × aa/(a × a).
1464 := (aaa + aa) × (aa + a)/(a × a).
1465 := ((aaa + aa) × (aa + a)/a + a)/a.
1466 := ((aaa + aa) × (aa + a)/a + a + a)/a.
1467 := ((aaa + a + a) × (aa + a + a)/a − a − a)/a.
1468 := ((aaa + a + a) × (aa + a + a)/a − a)/a.
1469 := (aaa + a + a) × (aa + a + a)/(a × a).
1470 := ((aaa + a + a) × (aa + a + a)/a + a)/a.
1471 := ((aaa + a + a) × (aa + a + a)/a + a + a)/a.
1472 := ((aaa + aa + aa + a) × aa/a − a − a)/a.
1473 := ((aaa + aa + aa + a) × aa/a − a)/a.
1474 := (aaa + aa + aa + a) × aa/(a × a).
1475 := ((aaa + aa + aa + a) × aa/a + a)/a.
1476 := (aaa + aa + a) × (aa + a)/(a × a).
1477 := ((aaa + aa + a) × (aa + a)/a + a)/a.
1478 := ((aaa + aa + a) × (aa + a)/a + a + a)/a.
1479 := (aaa × aaa/(aa − a − a) + aaa − a)/a.
1480 := (aaa × aaa/(aa − a − a) + aaa)/a.
1481 := (aaa × aaa/(aa − a − a) + aaa + a)/a.
14
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1482 := (aaa + a + a + a) × (aa + a + a)/(a × a).
1483 := ((aaa + a + a + a) × (aa + a + a)/a + a)/a.
1484 := ((aaa + a + a + a) × (aa + a + a)/a + a + a)/a.
1485 := (aaa + aa + aa + a + a) × aa/(a × a).
1486 := ((aaa + aa + aa + a + a) × aa/a + a)/a.
1487 := ((aaa + aa + a + a) × (aa + a)/a − a)/a.
1488 := (aaa + aa + a + a) × (aa + a)/(a × a).
1489 := ((aaa + aa + a + a) × (aa + a)/a + a)/a.
1490 := (aaa × aaa/(aa − a − a) + aaa + aa − a)/a.
1491 := (aaa × aaa/(aa − a − a) + aaa + aa)/a.
1492 := (aaa × aaa/(aa − a − a) + aaa + aa + a)/a.
1493 := (aaa/(a + a + a) × aaa − aaaa − aa + a)/(a + a).
1494 := ((aa + aa − a) × (aa + a + a) + aaa × aa)/(a × a).
1495 := (aaa + a + a + a + a) × (aa + a + a)/(a × a).
1496 := (aaaaaa × (a + a + a)/aaa − aa)/(a + a).
1497 := ((aa + aa + a) × (aa + a) + aaa × aa)/(a × a).
1498 := (aaa − a − a − a − a) × (aa + a + a + a)/(a × a).
1499 := ((aaaa − aaa) × (a + a + a)/(a + a) − a)/a.
1500 := (aaaa − aaa) × (a + a + a)/((a + a) × a).
1501 := ((aaaa − aaa) × (a + a + a)/(a + a) + a)/a.
1502 := (aaaaaa × (a + a + a)/aaa + a)/(a + a).
1503 := (aaaaaa + aaa)/aaa × (a + a + a)/(a + a).
1504 := ((aa + a + a + a + a) × aaaa/aa − aa)/a.
1505 := ((aaa + aa) × aaa/(a + a + a) + a)/(a + a + a).
1506 := ((aaaaa − aaa) × (a + a + a)/aa + aa + a)/(a + a).
1507 := (aaaa + aaa + aa)/(aa − a − a) × aa/a.
1508 := ((aaaa + aaa + aa)/(aa − a − a) × aa + a)/a.
1509 := ((aaa+aa)×aaa/(a+a+a)+aa+a+a)/(a+a+a).
1510 := ((aaaaa − a) × (a + a + a)/aa − aa + a)/(a + a).
1511 := ((aaa − a − a − a) × (aa + a + a + a)/a − a)/a.
1512 := (aaa − a − a − a) × (aa + a + a + a)/(a × a).
1513 := ((aaa − a − a − a) × (aa + a + a + a)/a + a)/a.
1514 := ((aa + a + a + a + a) × aaaa/aa − a)/a.
1515 := ((aa + a + a + a + a) × aaaa/aa)/a.
1516 := ((aa + a + a + a + a) × aaaa/aa + a)/a.
1517 := (aaa/(a + a + a) × aa + aaaa − a)/a.
1518 := (aaa/(a + a + a) × aa + aaaa)/a.
1519 := (aaa/(a + a + a) × aa + aaaa + a)/a.
1520 := (aaa/(a + a + a) × aa + aaaa + a + a)/a.
1521 := ((aaa − aa) × (a + a + a) + aaa × aa)/(a × a).
1522 := (((aaa − aa) × (a + a + a) + aaa × aa)/a + a)/a.
1523 := ((aaaa−a)×aa/(a+a)−aa−a−a)/(a+a+a+a).
1524 := ((aaaa−a)×aa/(a+a)−aa+a+a)/(a+a+a+a).
1525 := ((aa + a + a + a) × aaaa/aa + aaa)/a.
1526 := (aa + a + a + a) × (aaa − a − a)/(a × a).
1527 := ((aaaa − a) × aa/(a + a) + a + a + a)/(a + a + a + a).
1528 := ((aaaa + a)/(a + a + a + a) × aa − a − a)/(a + a).
1529 := ((aaaa + a)/(aa − a − a − a) × aa)/a.
1530 := (aaaa + aa) × (aa + a + a + a + a)/(aa × a).
1531 := ((aaaa + aa) × (aa + a + a + a + a)/aa + a)/a.
1532 := ((aaa − aa) × (a + a) + aaa × (aa + a))/(a × a).
1533 := ((aaa + aa − a − a − a − a) × (aa + a + a)/a − a)/a.
1534 := (aaa + aa − a − a − a − a) × (aa + a + a)/(a × a).
1535 := ((aaa + aa − a − a − a − a) × (aa + a + a)/a + a)/a.
1536 := (aaa×aaa−(a+a+a)×aa)/((aa−a−a−a)×a).
1537 := (aaaa + aaa)/(a + a) + (aaaaa + a)/(aa + a).
1538 := ((aa + a + a + a) × (aaa − a)/a − aa)/a.
1539 := ((aa + a + a + a) × (aaa − a)/a − a)/a.
1540 := (aa + a + a + a) × (aaa − a)/(a × a).
1541 := ((aa + a + a + a) × (aaa − a)/a + a)/a.
1542 := ((aa + a + a + a) × (aaa − a)/a + a + a)/a.
1543 := ((aaaa + aa) × aa/(a + a) + a)/(a + a + a + a).
1544 := ((aaa+aa−a−a−a)×(aa+a+a)/a−a−a−a)/a.
1545 := ((aaa + aa − a − a − a) × (aa + a + a)/a − a − a)/a.
1546 := ((aaa + aa − a − a − a) × (aa + a + a)/a − a)/a.
1547 := (aaa + aa − a − a − a) × (aa + a + a)/(a × a).
1548 := ((aaa + aa − a − a − a) × (aa + a + a)/a + a)/a.
1549 := ((aaa + aa − a − a − a) × (aa + a + a)/a + a + a)/a.
1550 := (aaa+aa+a+a)×(aaa−aa)/((aa−a−a−a)×a).
1551 := ((aa + a + a + a) × aaa/a − a − a − a)/a.
1552 := ((aa + a + a + a) × aaa/a − a − a)/a.
1553 := ((aa + a + a + a) × aaa/a − a)/a.
1554 := (aa + a + a + a) × aaa/(a × a).
1555 := ((aa + a + a + a) × aaa/a + a)/a.
1556 := ((aa + a + a + a) × aaa/a + a + a)/a.
1557 := ((aa + a + a + a) × aaa/a + a + a + a)/a.
1558 := ((aa + a + a + a) × aaa/a + a + a + a + a)/a.
1559 := (aa + a + a + a) × aaa/(a × a) + (aa − a)/(a + a).
1560 := (aaaaa − a)/aa + (aaaa − aa)/(a + a).
1561 := (aaa + aaa + a) × (aa + aa − a)/((a + a + a) × a).
1562 := aaaaaa/aaa + (aaaa + aa)/(a + a).
1563 := aaaaaa/aaa + (aaaa + aa)/(a + a) + a/a.
1564 := (aaaaa − aa − a)/aa + (aaaa − a)/(a + a).
1565 := (aaaaa − a)/aa + (aaaa − a)/(a + a).
1566 := (aaaaa − a)/aa + (aaaa + a)/(a + a).
1567 := ((aa + a + a + a) × (aaa + a)/a − a)/a.
1568 := (aa + a + a + a) × (aaa + a)/(a × a).
1569 := ((aa + a + a + a) × (aaa + a)/a + a)/a.
1570 := ((aa + a + a + a) × (aaa + a)/a + a + a)/a.
1571 := ((aa + a + a + a) × (aaa + a)/a + a + a + a)/a.
1572 := ((aaa + aa + aa + aa − a) × aa/a − a)/a.
1573 := (aaa + aa + aa + aa − a) × aa/(a × a).
1574 := ((aaa + aa + aa + aa − a) × aa/a + a)/a.
1575 := ((aaa + aa + aa + aa − a) × aa/a + a + a)/a.
1576 := ((aaa + aa + aa + aa − a) × aa/a + a + a + a)/a.
1577 := ((aaa + a) × (aa + a + a) + aa × aa)/(a × a).
1578 := (((aaa + a) × (aa + a + a) + aa × aa)/a + a)/a.
1579 := (((aaa + a) × (aa + a + a) + aa × aa)/a + a + a)/a.
1580 := ((aaa + aa + aa + aa) × aa/a − a − a − a − a)/a.
1581 := ((aaa + aa + aa + aa) × aa/a − a − a − a)/a.
1582 := ((aaa + aa + aa + aa) × aa/a − a − a)/a.
1583 := ((aaa + aa + aa + aa) × aa/a − a)/a.
1584 := (aaa + aa + aa + aa) × aa/(a × a).
1585 := ((aaa + aa) × (aa + a + a)/a − a)/a.
1586 := (aaa + aa) × (aa + a + a)/(a × a).
1587 := ((aaa + aa) × (aa + a + a)/a + a)/a.
1588 := (aaaaa + aaaaa + aa − a)/(aa + a + a + a).
1589 := (aaaaa + aa + a) × (a + a)/((aa + a + a + a) × a).
1590 := (aaa × aaa/(aa − a − a) + aaa + aaa − a)/a.
1591 := (aaa × aaa/(aa − a − a) + aaa + aaa)/a.
1592 := (aaa × aaa/(aa − a − a) + aaa + aaa + a)/a.
1593 := ((aaa + aa + aa) × (aa + a)/a − a − a − a)/a.
1594 := ((aaa + aa + aa) × (aa + a)/a − a − a)/a.
1595 := ((aaa + aa + aa) × (aa + a)/a − a)/a.
1596 := (aaa + aa + aa) × (aa + a)/(a × a).
1597 := ((aaa + aa + aa) × (aa + a)/a + a)/a.
1598 := ((aaa + aa + a) × (aa + a + a)/a − a)/a.
1599 := (aaa + aa + a) × (aa + a + a)/(a × a).
1600 := ((aaa + aa + a) × (aa + a + a)/a + a)/a.
1601 := ((aaa + aa + a) × (aa + a + a)/a + a + a)/a.
1602 := ((aaa + aa + a) × (aa + a + a)/a + a + a + a)/a.
1603 := ((aaa + aa + a) × (aa + a + a)/a + a + a + a + a)/a.
1604 := ((aaa + aa + aa + a) × (aa + a)/a − a − a − a − a)/a.
1605 := ((aaa + aa + aa + a) × (aa + a)/a − a − a − a)/a.
1606 := ((aaa + aa + aa + a) × (aa + a)/a − a − a)/a.
1607 := ((aaa + aa + aa + a) × (aa + a)/a − a)/a.
1608 := (aaa + aa + aa + a) × (aa + a)/(a × a).
1609 := ((aaa + aa + aa + a) × (aa + a)/a + a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1610 := ((aaa + aa + aa + a) × (aa + a)/a + a + a)/a.
1611 := (aaaa + aaaa + aaaa − aaa)/(a + a).
1612 := (aaa + aa + a + a) × (aa + a + a)/(a × a).
1613 := ((aaa + aa + a + a) × (aa + a + a)/a + a)/a.
1614 := ((aaa + aa + a + a) × (aa + a + a)/a + a + a)/a.
1615 := ((aaa + aa + a + a) × (aa + a + a)/a + a + a + a)/a.
1616 := (aa + aa + aa − a) × aaaa/(aa × (a + a)).
1617 := (aa + aa + aa − a) × aaaa/(aa × (a + a)) + a/a.
1618 := ((aaa + aa + aa + a + a) × (aa + a)/a − a − a)/a.
1619 := ((aaa + aa + aa + a + a) × (aa + a)/a − a)/a.
1620 := (aaa + aa + aa + a + a) × (aa + a)/(a × a).
1621 := ((aaa + aa + aa + a + a) × (aa + a)/a + a)/a.
1622 := ((aaa + aa + aa + a + a) × (aa + a)/a + a + a)/a.
1623 := ((aaa + aa + aa + a + a) × (aa + a)/a + a + a + a)/a.
1624 := (aaaa + aaaa + aa) × (aa − a − a − a)/(aa × a).
1625 := (aaa + aa + a + a + a) × (aa + a + a)/(a × a).
1626 := ((aa + a + a + a + a) × aaaa/aa + aaa)/a.
1627 := ((aaa + aaa) × (aa + aa)/(a + a + a) − a)/a.
1628 := (aaa + aaa) × (aa + aa)/((a + a + a) × a).
1629 := ((aaa + aaa) × (aa + aa)/(a + a + a) + a)/a.
1630 := (aaa/(a + a + a) × aa + aaaa + aaa + a)/a.
1631 := (aaa + aaa + aa) × (aa + aa − a)/((a + a + a) × a).
1632 := (aaa + aa + aa + a + a + a) × (aa + a)/(a × a).
1633 := ((aaa + aa + aa + a + a + a) × (aa + a)/a + a)/a.
1634 := (aaaaaa + a)/(aa + aa + aa + a) × a/(a + a).
1635 := (aa + a + a + a + a) × (aaa − a − a)/(a × a).
1636 := ((aa + a + a + a) × aaaa/aa + aaa + aaa)/a.
1637 := ((aa + a + a + a) × aaaa/aa + aaa + aaa + a)/a.
1638 := (aaa − aa − aa − aa) × (aa + aa − a)/(a × a).
1639 := (aaaa × (aa + a)/(a + a) − aaa + a)/(a + a + a + a).
1640 := ((aaa + aa + aa) × aaa/(a + a + a) − a)/(a + a + a).
1641 := ((aaa − aa − aa) × aaa/(a + a + a) − aa)/(a + a).
1642 := ((aaa − aa) × (a + a + a) + (aaa + aa) × aa)/(a × a).
1643 := ((aaa + aaa − aa) × (a + a) + aaa × aa)/(a × a).
1644 := (((aaa + aaa − aa) × (a + a) + aaa × aa)/a + a)/a.
1645 := ((aaaa−aa)×(a+a+a)/(a+a)−a−a−a−a−a)/a.
1646 := ((aaa − aa − aa) × aaa/(a + a + a) − a)/(a + a).
1647 := ((aaa − aa − aa) × aaa/(a + a + a) + a)/(a + a).
1648 := ((aaaa − aa) × (a + a + a)/(a + a) − a − a)/a.
1649 := ((aaaa − aa) × (a + a + a)/(a + a) − a)/a.
1650 := (aaaa − aa) × (a + a + a)/((a + a) × a).
1651 := ((aa + aa + aa) × (aaa − aa)/(a + a) + a)/a.
1652 := ((aa + aa + aa) × (aaa − aa)/(a + a) + a + a)/a.
1653 := ((aa + aa + aa) × (aaa − aa)/(a + a) + a + a + a)/a.
1654 := ((aa+aa+aa)×(aaa−aa)/(a+a)+a+a+a+a)/a.
1655 := (aaaaa − aaa)/(aa − a) + (aaaa − a)/(a + a).
1656 := (aaaaa − aaa)/(aa − a) + (aaaa + a)/(a + a).
1657 := ((aaaa + a) × (a + a + a)/(a + a) − aa)/a.
1658 := ((aaaa + a) × (a + a + a)/(a + a) − aa + a)/a.
1659 := ((aaaa + a) × (a + a + a)/(a + a) − aa + a + a)/a.
1660 := (aaaa + aaaa + aaaa − aa − a − a)/(a + a).
1661 := (aaaa + aaaa + aaaa − aa)/(a + a).
1662 := ((aa + a + a + a + a) × aaa/a − a − a − a)/a.
1663 := ((aa + a + a + a + a) × aaa/a − a − a)/a.
1664 := ((aa + a + a + a + a) × aaa/a − a)/a.
1665 := (aa + a + a + a + a) × aaa/(a × a).
1666 := (aaaa + aaaa + aaaa − a)/(a + a).
1667 := (aaaa + aaaa + aaaa + a)/(a + a).
1668 := (aaaa + a) × (a + a + a)/((a + a) × a).
1669 := ((aaaa + a) × (a + a + a)/(a + a) + a)/a.
1670 := ((aaaa + a) × (a + a + a)/(a + a) + a + a)/a.
1671 := ((aaaa + a) × (a + a + a)/(a + a) + a + a + a)/a.
1672 := (aaaa + aaaa + aaaa + aa)/(a + a).
1673 := (aaaa + aaaa + aaaa + aa + a + a)/(a + a).
15
1674 := (((aa + a + a + a) × aaa + aa × aa)/a − a)/a.
1675 := ((aa + a + a + a) × aaa + aa × aa)/(a × a).
1676 := (((aa + a + a + a) × aaa + aa × aa)/a + a)/a.
1677 := ((aa + a + a + a + a) × (aaa + a)/a − a − a − a)/a.
1678 := ((aa + a + a + a + a) × (aaa + a)/a − a − a)/a.
1679 := ((aa + a + a + a + a) × (aaa + a)/a − a)/a.
1680 := (aa + a + a + a + a) × (aaa + a)/(a × a).
1681 := ((aa + a + a + a + a) × (aaa + a)/a + a)/a.
1682 := ((aaaa + aa) × (a + a + a)/(a + a) − a)/a.
1683 := (aaaa + aa) × (a + a + a)/((a + a) × a).
1684 := ((aaaa + aa) × (a + a + a)/(a + a) + a)/a.
1685 := ((aaaa + aa) × (a + a + a)/(a + a) + a + a)/a.
1686 := ((aaa + aa) × (aa + a) + aaa × (a + a))/(a × a).
1687 := ((aaa + aaa − aa) × (aa − a − a − a)/a − a)/a.
1688 := (aaa + aaa − aa) × (aa − a − a − a)/(a × a).
1689 := ((aaa + aaa − aa) × (aa − a − a − a)/a + a)/a.
1690 := ((aaa + aaa − aa) × (aa − a − a − a)/a + a + a)/a.
1691 := (aaa − aa − aa) × (aa + aa − a − a − a)/(a × a).
1692 := ((aaa − aa − aa) × (aa + aa − a − a − a)/a + a)/a.
1693 := ((aaa + aa) × aaa/(a + a) + a)/(a + a + a + a).
1694 := ((aaa + a)/(a + a) × aa × aa)/((a + a + a + a) × a).
1695 := ((aaa+aa)×aaa/(a+a)+aa−a−a)/(a+a+a+a).
1696 := ((aaa+aa)×aaa/(a+a)+aa+a+a)/(a+a+a+a).
1697 := (aaaa×(aa+a)/(a+a)+aaa+aa)/(a+a+a+a).
1698 := ((aaa + a) × aaa/(a + a) − aaaa − aa)/(a + a + a).
1669 := ((aa + aa + aa + a) × (aaa − aa)/(a + a) − a)/a.
1700 := (aa + aa + aa + a) × (aaa − aa)/((a + a) × a).
1701 := ((aa + aa + aa + a) × (aaa − aa)/(a + a) + a)/a.
1702 := (aaa + aaa) × (aa + aa + a)/((a + a + a) × a).
1703 := ((aaa + a) × aaa/(aa + aa − a) + aaaa)/a.
1674 := ((aaa + aa + aa + aa + aa) × aa/a − a)/a.
1705 := (aaa + aa + aa + aa + aa) × aa/(a × a).
1706 := ((aa + a + a + a) × (aaa + aa)/a − a − a)/a.
1707 := ((aa + a + a + a) × (aaa + aa)/a − a)/a.
1708 := (aa + a + a + a) × (aaa + aa)/(a × a).
1709 := ((aa + a + a + a) × (aaa + aa)/a + a)/a.
1710 := ((aa + a + a + a) × (aaa + aa)/a + a + a)/a.
1711 := ((aaa − aa) × (aa + a)/(a + a) + aaaa)/a.
1712 := ((aaa − aa) × (aa + a)/(a + a) + aaaa + a)/a.
1713 := ((aaa − a) × aa/(a + a) + aaaa − a − a − a)/a.
1714 := ((aaa − a) × aa/(a + a) + aaaa − a − a)/a.
1715 := ((aaa − a) × aa/(a + a) + aaaa − a)/a.
1716 := ((aaa − a) × aa/(a + a) + aaaa)/a.
1717 := ((aaa − a) × aa/(a + a) + aaaa + a)/a.
1718 := ((aaa − a) × aa/(a + a) + aaaa + a + a)/a.
1719 := ((aaa − a) × aa/(a + a) + aaaa + a + a + a)/a.
1720 := ((aaa + aa + a) × (aa + a + a + a)/a − a − a)/a.
1721 := ((aaa + aa + a) × (aa + a + a + a)/a − a)/a.
1722 := (aaa + aa + a) × (aa + a + a + a)/(a × a).
1723 := ((aaa + aa + a) × (aa + a + a + a)/a + a)/a.
1724 := ((aaa + aa + a) × (aa + a + a + a)/a + a + a)/a.
1725 := ((aaa + a)/(a + a) × aa + aaaa − a − a)/a.
1726 := (((((aaa + a)/(a + a)) × aa) + aaaa) − a)/a.
1727 := ((((aaa + a)/(a + a)) × aa) + aaaa)/a.
1728 := ((((aaa + aa) + aa) + aa) × (aa + a))/(a × a).
1729 := (aaa + aa + aa) × (aa + a + a)/(a × a).
1730 := ((aaa + aa + aa) × (aa + a + a)/a + a)/a.
1731 := ((aaa + aa + aa) × (aa + a + a)/a + a + a)/a.
1732 := ((aaa + aa + aa) × (aa + a + a)/a + a + a + a)/a.
1733 := ((aaa + aa + aa) × (aa + a + a)/a + a + a + a + a)/a.
1734 := (aaaa + aa)/aa × (aa + aa + aa + a)/(a + a).
1735 := ((aaa + aa + a + a) × (aa + a + a + a)/a − a)/a.
1736 := (aaa + aa + a + a) × (aa + a + a + a)/(a × a).
1737 := ((aaa + aa + a + a) × (aa + a + a + a)/a + a)/a.
16
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1738 := ((aaa + aa + a + a) × (aa + a + a + a)/a + a + a)/a.
1739 := ((aaa+aa+a+a)×(aa+a+a+a)/a+a+a+a)/a.
1740 := ((aaaaa + a)/(aa + a) × (a + a) − aaa − a)/a.
1741 := ((aaaaa + a)/(aa + a) × (a + a) − aaa)/a.
1742 := (aaa + aa + aa + a) × (aa + a + a)/(a × a).
1743 := ((aaa + aa + aa + a) × (aa + a + a)/a + a)/a.
1744 := ((aaa + aa + aa + a) × (aa + a + a)/a + a + a)/a.
1745 := ((aaa + aa + aa + a) × (aa + a + a)/a + a + a + a)/a.
1746 := ((aaaaa + aaaa) × (a + a))/((aa + a + a + a) × a).
1747 := ((aaaa+a+a)×(aa+aa)/(aa+a+a+a)−a−a)/a.
1748 := ((aaaa + a + a) × (aa + aa)/(aa + a + a + a) − a)/a.
1749 := (aaaa + a + a) × (aa + aa)/((aa + a + a + a) × a).
1750 := (aaa − aaaa) × (a − aa − aa)/((aa + a) × a).
1751 := ((aaa − aaaa) × (a − aa − aa)/(aa + a) + a)/a.
1752 := (aaaa − aaa − aaa − aa − a − a) × (a + a)/(a × a).
1753 := ((aaaa − aaa − aaa − aa − a) × (a + a)/a − a)/a.
1754 := (aaaa − aaa − aaa − aa − a) × (a + a)/(a × a).
1755 := (aaa + aa + aa + a + a) × (aa + a + a)/(a × a).
1756 := (aaaa − aaa − aaa − aa) × (a + a)/(a × a).
1757 := ((aaaa − aaa − aaa − aa) × (a + a)/a + a)/a.
1758 := (aaaa − aaa − aaa − aa + a) × (a + a)/(a × a).
1759 := ((aaaa − aaa − aaa − aa + a) × (a + a)/a + a)/a.
1760 := (aa+aa+aa−a)×(aaaa−aa)/((aa−a)×(a+a)).
1761 := ((aaaa−aaa−aaa−aa+a)×(a+a)/a+a+a+a)/a.
1762 := ((aa + aa + aa + a + a) × aaaa/aa − aa)/(a + a).
1763 := (aaaaaa/(aa + aa − a) × a + a)/(a + a + a) − a/a.
1764 := (aaaaaa/(aa + aa − a) × a + a)/(a + a + a).
1765 := (aaa × (aa + a)/(a + a) + aaaa − aa − a)/a.
1766 := (aaa × (aa + a)/(a + a) + aaaa − aa)/a.
1767 := ((aa + aa + aa + a + a) × aaaa/aa − a)/(a + a).
1768 := (aaa + aaa − a) × (aa − a − a − a)/(a × a).
1769 := ((aaa + aaa − a) × (aa − a − a − a)/a + a)/a.
1770 := ((aaa + aaa − a) × (aa − a − a − a)/a + a + a)/a.
1771 := (aaaaa − a − a) × aa/((aa + aa + a) × (a + a + a)).
1772 := ((aaa + aaa) × (aa − a − a − a)/a − a − a − a − a)/a.
1773 := ((aaa + aaa) × (aa − a − a − a)/a − a − a − a)/a.
1774 := ((aaa + aaa) × (aa − a − a − a)/a − a − a)/a.
1775 := ((aaa + aaa) × (aa − a − a − a)/a − a)/a.
1776 := (aaa + aaa) × (aa − a − a − a)/(a × a).
1777 := (aaa × (aa + a)/(a + a) + aaaa)/a.
1778 := (aaaa − aaa − aaa) × (a + a)/(a × a).
1779 := ((aaaa − aaa − aaa) × (aa + aa)/aa + a)/a.
1780 := (aaaa − aaa − aaa + a) × (a + a)/(a × a).
1781 := ((aaa + aa) × aa/(a + a) + aaaa − a)/a.
1782 := ((aaa + aa) × aa/(a + a) + aaaa)/a.
1783 := ((aaa + a) × (aa + a)/(a + a) + aaaa)/a.
1784 := (aaa + aaa + a) × (aa − a − a − a)/(a × a).
1785 := (aa + aa + aa + a + a) × (aaaa + aa)/(aa × (a + a)).
1786 := ((aaa + aaa) × (a + a) + (aaa + aa) × aa)/(a × a).
1787 := (aaa × (aa + a)/(a + a) + aaaa + aa − a)/a.
1788 := (aaa × (aa + a)/(a + a) + aaaa + aa)/a.
1789 := (aaa × (aa + a)/(a + a) + aaaa + aa + a)/a.
1790 := (aaa × (aa + a)/(a + a) + aaaa + aa + a + a)/a.
1791 := ((aa + aa + aa − a) × (aaa + a)/(a + a) − a)/a.
1792 := (aa + aa + aa − a) × (aaa + a)/((a + a) × a).
1793 := ((aa + aa + aa − a) × (aaa + a)/(a + a) + a)/a.
1794 := (aaa+aaa+aa+a)×(aa+aa+a)/((a+a+a)×a).
1795 := ((aaaaa − aaaa − aaa)/aa × (a + a) − a − a − a)/a.
1796 := ((aaaaa − aaaa − aaa)/aa × (a + a) − a − a)/a.
1797 := ((aaaaa − aaaa − aaa)/aa × (a + a) − a)/a.
1798 := (aaaaa − aaaa − aaa)/aa × (a + a)/a.
1799 := ((aaaaa − aaaa − aaa)/aa × (a + a) + a)/a.
1800 := (aaaa − aaa − aaa + aa) × (a + a)/(a × a).
1801 := ((aaaa − aaa − aaa + aa) × (a + a)/a + a)/a.
1802 := (aaaa − aaa − aaa + aa + a) × (a + a)/(a × a).
1803 := ((aaaa − aaa − aaa + aa + a) × (a + a)/a + a)/a.
1804 := ((aaaa−a)×(aa+a+a)/(a+a)+a)/(a+a+a+a).
1805 := ((aaaaa − aaaa − aa − a) ∗ (a + a)/aa − aa)/a.
1806 := ((aaaaa − aaaa − aa − a) ∗ (a + a)/aa − aa + a)/a.
1807 := (aaaa + a) × (aa + a + a)/((a + a) × (a + a + a + a)).
1808 := ((aaa + aa) × (aa + a + a) + aaa × (a + a))/(a × a).
1809 := (aaaa/aa × (a + a) − a) × (aa − a − a)/(a × a).
1810 := ((aaaa/aa × (a + a) − a) × (aa − a − a)/a + a)/a.
1811 := (((aaa − a) × aa/(a + a) − a) × (a + a + a)/a − a)/a.
1812 := ((aaa − a) × aa/(a + a) − a) × (a + a + a)/(a × a).
1813 := (aaa − aa − a − a) × aaa/((a + a + a) × (a + a)).
1814 := (((aaa−a)×aa/(a+a)−a)×(a+a+a)/a+a+a)/a.
1815 := (aa + aa + aa) × (aaaa − aa)/((a + a) × (aa − a)).
1816 := (aaaaa − aaaa − aa − a) × (a + a)/(aa × a).
1817 := ((aaaaa − aaaa − a)/aa × (a + a) − a)/a.
1818 := aaaa × (aa − a − a) × (a + a)/(aa × a × a).
1819 := ((aaaaa − aaaa − a)/aa × (a + a) + a)/a.
1820 := (aaaa × (aa − a − a)/aa + a) × (a + a)/(a × a).
1821 := ((aaaaaaa − a)/aaa × (a + a) + aa)/aa.
1822 := (aaaa − aaa − aaa + aa + aa) × (a + a)/(a × a).
1823 := ((aaaa − aaa − aaa + aa + aa) × (a + a)/a + a)/a.
1824 := ((aaa+aaa−a−a−a)×(aaa−aa)/(aa+a)−a)/a.
1825 := (aaa + aaa − a − a − a) × (aaa − aa)/((aa + a) × a).
1826 := (aaa + aaa + aaa − a) × aa/((a + a) × a).
1827 := ((aaa − a) × aa/(a + a) + aaaa + aaa)/a.
1828 := ((aaa − a) × aa/(a + a) + aaaa + aaa + a)/a.
1829 := ((aaaaa − aaaa − a)/aa × (a + a) + aa)/a.
1830 := (aa + a + a + a + a) × (aaa + aa)/(a × a).
1831 := ((aa + a + a + a + a) × (aaa + aa)/a + a)/a.
1832 := ((aaaa + aaa) × (a + a + a)/(a + a) − a)/a.
1833 := (aaaa + aaa) × (a + a + a)/((a + a) × a).
1834 := ((aaaa + aaa) × (a + a + a)/(a + a) + a)/a.
1835 := (aaaa − aa + a) × (aa − a)/((a + a) × (a + a + a)).
1836 := (aaaaaa − aa − aa − aa) × (a + a)/(aa × aa).
1837 := ((aaaaaa + aa + aa)/aa × (a + a) + a)/aa.
1838 := ((aaaaa − aa)/(aa + a) × (a + a) − aa − a)/a.
1839 := ((aaaaa − aa)/(aa + a) × (a + a) − aa)/a.
1840 := ((aaaaa − aa)/(aa + a) × (a + a) − aa + a)/a.
1841 := ((aaaaa + a)/(aa + a) × (a + a) − aa)/a.
1842 := ((aaaaa + a)/(aa + a) × (a + a) − aa + a)/a.
1843 := ((aaa + aa) × (aa + a)/(a + a) + aaaa)/a.
1844 := ((aaaa + aaa) × (a + a + a)/(a + a) + aa)/a.
1845 := (aaa + aa + a) × (aa + a + a + a + a)/(a × a).
1846 := ((aa + aa + aa) × (aaa + a)/(a + a) − a − a)/a.
1847 := ((aa + aa + aa) × (aaa + a)/(a + a) − a)/a.
1848 := (aa + aa + aa) × (aaa + a)/((a + a) × a).
1849 := ((aaaaa − aa)/(aa + a) × (a + a) − a)/a.
1850 := (aaaaa − aa) × (a + a)/((aa + a) × a).
1851 := ((aaaaa + a)/(aa + a) × (a + a) − a)/a.
1852 := (aaaaa + a) × (a + a)/((aa + a) × a).
1853 := ((aaaaa + a)/(aa + a) × (a + a) + a)/a.
1854 := ((aaaaa + a)/(aa + a) × (a + a) + a + a)/a.
1855 := (aaaa + a + a) × (aa + aa − a − a)/((aa + a) × a).
1856 := (aaa + aaa + aa − a) × (aa − a − a − a)/(a × a).
1857 := ((aaaa − aaa − aa) × (a + a) − aa × aa)/(a × a).
1858 := (((aaaa − aaa − aa) × (a + a) − aa × aa)/a + a)/a.
1859 := ((aaa + aa + aa + aa + aa) × (aa + a)/a − a)/a.
1860 := (aaa + aa + aa + aa + aa) × (aa + a)/(a × a).
1861 := ((aaaaa − aa)/(aa + a) × (a + a) + aa)/a.
1862 := (aaa + aa + aa) × (aa + a + a + a)/(a × a).
1863 := ((aaaaa + a)/(aa + a) × (a + a) + aa)/a.
1864 := (aaa + aaa + aa) × (aa − a − a − a)/(a × a).
1865 := ((aaa + aaa + aa) × (aa − a − a − a)/a + a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1866 := ((aaa − aa) × (aaa + a)/(a + a) − a − a)/(a + a + a).
1867 := ((aaa − aa) × (aaa + a)/(a + a) + a)/(a + a + a).
1868 := (aaaa × aaa/(aa + aa + aa) − a)/(a + a).
1869 := (aaa − aa − aa) × (aa + aa − a)/(a × a).
1870 := (aaaaa + aaa − a − a) × (a + a)/((aa + a) × a).
1871 := (aaaaa+aaa+a+a+a+a)×(a+a)/((aa+a)×a).
1872 := (aaa + aa + aa + aa) × (aa + a + a)/(a × a).
1873 := ((aaaaa + a)/(aa + a) × (a + a) + aa + aa − a)/a.
1874 := ((aaaaa + a)/(aa + a) × (a + a) + aa + aa)/a.
1875 := (aaaa+aa+a+a+a)×(aa−a)/((a+a)×(a+a+a)).
1876 := (aaaa/aa × (a + a) − a) × (aaa + a)/((aa + a) × a).
1877 := ((aaaa − aaa − a) × (a + a) − aa × aa)/(a × a).
1878 := ((aaaaa − aaa) × (a + a)/aa − aaa − aa)/a.
1879 := ((aaaa − aaa) × (a + a) − aa × aa)/(a × a).
1880 := (aaaaaa/aaa × (a + a) − aaa − aa)/a.
1881 := (aaaa + aaaa + a) × aa/((aa + a + a) × a).
1882 := ((aaa + a) × aaaa/(aa + aa) − aa + a)/(a + a + a).
1883 := ((aaa + a + a) × (aaa − aa)/(a + a) − a)/(a + a + a).
1884 := ((aa + aa + aa + a) × aaa/(a + a) − a − a − a)/a.
1885 := ((aa + aa + aa + a) × aaa/(a + a) − a − a)/a.
1886 := ((aa + aa + aa + a) × aaa/(a + a) − a)/a.
1887 := (aa + aa + aa + a) × aaa/((a + a) × a).
1888 := ((aaaaa − aaa) × (a + a)/aa − aaa − a)/a.
1889 := ((aaaaa − aaa) × (a + a)/aa − aaa)/a.
1890 := (aaaaaa/aaa × (a + a) − aaa − a)/a.
1891 := (aaaaaa/aaa × (a + a) − aaa)/a.
1892 := (aaaaaa/aaa × (a + a) − aaa + a)/a.
1893 := (aaaaaa/aaa × (a + a) − aaa + a + a)/a.
1894 := (aaaaaa/aaa × (a + a) − aaa + a + a + a)/a.
1895 := (aaaaaa/aaa × (a + a) − aaa + a + a + a + a)/a.
1896 := ((aa + aa − a) × aaaaa/(aaa + aa + a) − a)/a.
1897 := ((aa − aaa − aaa) × (a − aa + a)/a − a − a)/a.
1898 := ((aa − aaa − aaa) × (a − aa + a)/a − a)/a.
1899 := (aa − aaa − aaa) × (a − aa + a)/(a × a).
1900 := (aa + aa − a − a − a) × (aaa − aa)/(a × a).
1901 := ((aa + aa − a − a − a) × (aaa − aa)/a + a)/a.
1902 := (aaaaaa/aaa × (a + a) − aaa + aa)/a.
1903 := (aaaaaa/aaa × (a + a) − aaa + aa + a)/a.
1904 := (aa + aa + aa + a) × (aaa + a)/((a + a) × a).
1905 := ((aa + aa + aa + a) × (aaa + a)/(a + a) + a)/a.
1906 := ((aa + aa + aa + a) × (aaa + a)/(a + a) + a + a)/a.
1907 := ((aaaaa − aa − a)/aa × (a + a) − aaa)/a.
1908 := ((aaaa + aaaa) × (aa − a)/aa − aaa − a)/a.
1909 := ((aaaaa − a)/aa × (a + a) − aaa)/a.
1910 := ((aaaaa − a)/aa × (a + a) − aaa + a)/a.
1911 := (aaaaaa × (aa + aa − a)/aaa)/aa.
1912 := (aaaaaa × (aa + aa − a)/aaa + aa)/aa.
1913 := ((aaa − aa − aa − a − a) × (aa + aa)/a − a)/a.
1914 := (aaa − aa − aa − a − a) × (aa + aa)/(a × a).
1915 := ((aaa − aa − aa − a − a) × (aa + aa)/a + a)/a.
1916 := ((aa + aa − a − a − a) × aaaa/aa − a − a − a)/a.
1917 := ((aa + aa − a − a − a) × aaaa/aa − a − a)/a.
1918 := ((aa + aa − a − a − a) × aaaa/aa − a)/a.
1919 := (aa + aa − a − a − a) × aaaa/(aa × a).
1920 := ((aa + aa − a − a − a) × aaaa/aa + a)/a.
1921 := (aaa + aaa − a) × (aaa + a + a)/((aa + a + a) × a).
1922 := ((aa − aaa) × (a + a + a) + aaaa × (a + a))/(a × a).
1923 := ((aaaa − a) × (aa + aa)/(aa + a) − aaa − a)/a.
1924 := ((aaaa − a) × (aa + aa)/(aa + a) − aaa)/a.
1925 := (aa − aaaa) × (a − aa − aa)/((aa + a) × a).
1926 := ((aa − aaaa) × (a − aa − aa)/(aa + a) + a)/a.
1927 := ((aa − aaaa) × (a − aa − aa)/(aa + a) + a + a)/a.
1928 := ((a − aaaaa) × (a − aa − aa)/aa − a − a)/aa.
1929 := ((aaaaa − aaaa − a)/aa × (a + a) + aaa)/a.
17
1930 := ((aa + aa − a − a − a) × aaaa/aa + aa)/a.
1931 := ((aa + aa − a − a − a) × aaaa/aa + aa + a)/a.
1932 := (aaaa − aaa + aa + a) × (aa + aa − a)/(aa × a).
1933 := ((aaaa − aaa − aa − aa − aa) × (a + a)/a − a)/a.
1934 := (aaaa − aaa − aa − aa − aa) × (a + a)/(a × a).
1935 := (aaaaa − aa)/(aa + a) + (aaaaa − a)/aa.
1936 := (aaa − aa − aa − a) × (aa + aa)/(a × a).
1937 := ((aaa − aa − aa − a) × (aa + aa)/a + a)/a.
1938 := (aa + aa − a − a − a) × (aaaa + aa)/(aa × a).
1939 := (a − aaaa + a + a) × (a − aa − aa)/((aa + a) × a).
1940 := ((aaaaa−a−a)/(aa+aa−a)×aa+a)/(a+a+a).
1941 := ((aa + aa − a − a − a) × aaaa/aa + aa + aa)/a.
1942 := ((aaaa+aaa)×(a+a+a)/(a+a)+aaa−a−a)/a.
1943 := ((aaaa + aaa) × (a + a + a)/(a + a) + aaa − a)/a.
1944 := ((aaaa + aaa) × (a + a + a)/(a + a) + aaa)/a.
1945 := ((aa + aa − a) × (aaaa + a)/(aa + a) − a)/a.
1946 := (aa + aa − a) × (aaaa + a)/((aa + a) × a).
1947 := ((aa + aa − a) × (aaaa + a)/(aa + a) + a)/a.
1948 := ((aa + aa − a) × (aaaa + a)/(aa + a) + a + a)/a.
1949 := ((aaa − aa − aa) × (aa + aa)/a + a − aa + a)/a.
1950 := ((aaaaa − aa)/(aa + a) × (a + a) + aaa − aa)/a.
1951 := ((aa + aa + aa − a) × (aaa + aa)/(a + a) − a)/a.
1952 := (aa + aa + aa − a) × (aaa + aa)/((a + a) × a).
1953 := (aaa/(a + a + a) × aaa + a)/(a + a) − aaaa/aa.
1954 := (aaaa − aaa − aa − aa − a) × (a + a)/(a × a).
1955 := ((aaaa − aaa − aa − aa) × (a + a)/a − a)/a.
1956 := (aaaa − aaa − aa − aa) × (a + a)/(a × a).
1957 := ((aaa − aa − aa) × (aa + aa)/a − a)/a.
1958 := (aaa − aa − aa) × (aa + aa)/(a × a).
1959 := ((aaa − aa − aa) × (aa + aa)/a + a)/a.
1960 := (aaa + aaa − aa − a) × (aaa + a)/((aa + a) × a).
1961 := ((aaaaa − aa)/(aa + a) × (a + a) + aaa)/a.
1962 := ((aaaaa + a)/(aa + a) × (a + a) + aaa − a)/a.
1963 := ((aaaaa + a)/(aa + a) × (a + a) + aaa)/a.
1964 := ((aaaaa + a)/(aa + a) × (a + a) + aaa + a)/a.
1965 := ((aaaaa + a)/(aa + a) × (a + a) + aaa + a + a)/a.
1966 := ((aaaa+aa+a+a)×(aa+aa−a)/(aa+a)−a)/a.
1967 := (aaaa + aa + a + a) × (aa + aa − a)/((aa + a) × a).
1967 := ((aaa − aa − aa) × (aa + aa)/a + aa − a)/a.
1969 := ((aaa − aa − aa) × (aa + aa)/a + aa)/a.
1970 := ((aaa − aa − aa) × (aa + aa)/a + aa + a)/a.
1971 := ((aaa − aa − aa) × (aa + aa)/a + aa + a + a)/a.
1972 := ((aaaa − aaa − aa − a − a) × (a + a)/a − a − a)/a.
1973 := ((aaaa − aaa − aa − a − a) × (a + a)/a − a)/a.
1974 := (aaaa − aaa − aa − a − a) × (a + a)/(a × a).
1975 := ((aaaa − aaa − aa − a − a) × (a + a)/a + a)/a.
1976 := (aaaa − aaa − aa − a) × (a + a)/(a × a).
1977 := ((aaaa − aaa − aa) × (aa + aa)/aa − a)/a.
1978 := (aaaa − aaa − aa) × (a + a)/(a × a).
1979 := ((aaaa − aaa − aa) × (a + a)/a + a)/a.
1980 := ((aaaa − aaa − aa) × (a + a)/a + a + a)/a.
1981 := ((aaaa − aaa − aa + a + a) × (a + a)/a − a)/a.
1982 := (aaaa − aaa − aa + a + a) × (a + a)/(a × a).
1983 := ((aaaa − aaa − aa + a + a) × (a + a)/a + a)/a.
1984 := ((aaaa − aaa − aa + a + a) × (a + a)/a + a + a)/a.
1985 := ((aaaa − aaa − a − a) × (aa + aa)/aa − aa)/a.
1986 := ((aaaaa − aaa − aa) × (a + a)/aa − aa − a)/a.
1987 := ((aaaaa − aaa − aa) × (a + a)/aa − aa)/a.
1988 := ((aaaaa − aaa) × (a + a)/aa − aa − a)/a.
1989 := ((aaaaa − aaa) × (a + a)/aa − aa)/a.
1990 := (aaaaaa/aaa × (a + a) − aa − a)/a.
1991 := (aaaaaa/aaa × (a + a) − aa)/a.
1992 := (aaaaaa/aaa × (a + a) − aa + a)/a.
1993 := ((aaaaaa + aaa)/aaa × (a + a) − aa)/a.
18
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1994 := (aaaa − aaa − a − a − a) × (a + a)/(a × a).
1995 := ((aaaa − aaa − a − a) × (a + a)/a − a)/a.
1996 := (aaaa − aaa − a − a) × (a + a)/(a × a).
1997 := ((aaaaa − aaa − aa) × (a + a)/aa − a)/a.
1998 := (aaaa − aaa − a) × (a + a)/(a × a).
1999 := ((aaaaa − aaa) × (a + a)/aa − a)/a.
2000 := (aaaa − aaa) × (a + a)/(a × a).
2001 := (aaaaaa/aaa × (a + a) − a)/a.
2002 := aaaaaa/aaa × (a + a)/a.
2003 := (aaaaaa/aaa × (a + a) + a)/a.
2004 := (aaaa − aaa + a + a) × (a + a)/(a × a).
2005 := (aaaaaa/aaa × (a + a) + a + a + a)/a.
2006 := ((aaa + aaa + a) × (aa − a − a)/a − a)/a.
2007 := (aaa + aaa + a) × (aa − a − a)/(a × a).
2008 := ((aaa + aaa + a) × (aa − a − a)/a + a)/a.
2009 := ((aaaaa − a) × (a + a) − aa × aa)/(aa × a).
2010 := (aaaaa + aaaaa − aaa − a)/aa.
2011 := ((aaaaa − aaa) × (a + a)/aa + aa)/a.
2012 := ((aaaaaa/aaa) × (a + a) + aa − a)/a.
2013 := (aaaaaa/aaa × (a + a) + aa)/a.
2014 := (aaaaaa/aaa × (a + a) + aa + a)/a.
2015 := (aaaaaa/aaa × (a + a) + aa + a + a)/a.
2016 := ((aaaaa − aa − a)/aa × (a + a) − a − a)/a.
2017 := ((aaaaa − aa − a)/aa × (a + a) − a)/a.
2018 := (aaaaa − aa − a)/aa × (a + a)/a.
2019 := ((aaaaa − a)/aa × (a + a) − a)/a.
2020 := (aaaaa − a)/aa × (a + a)/a.
2021 := ((aaaaa − a)/aa × (a + a) + a)/a.
2022 := (aaaa − aaa + aa) × (a + a)/(a × a).
2023 := (aaaaaa/aaa × (a + a) + aa + aa − a)/a.
2024 := (aaaa − aaa + aa + a) × (a + a)/(a × a).
2025 := ((aaaa − aaa + aa + a) × (a + a)/a + a)/a.
2026 := (aaaa − aaa + aa + a + a) × (a + a)/(a × a).
2027 := ((aaaa − aaa + aa + a + a) × (a + a)/a + a)/a.
2028 := ((aaaa − a) × aa/(a + a) − aa − aa + a)/(a + a + a).
2029 := ((aaaaa − aa − a)/aa × (a + a) + aa)/a.
2030 := ((aaaaa − a)/aa × (a + a) + aa − a)/a.
2031 := ((aaaaa − a)/aa × (a + a) + aa)/a.
2032 := ((aaaaa − a)/aa × (a + a) + aa + a)/a.
2033 := ((aaa × aaa − aa × aa)/(a + a) − a)/(a + a + a).
2034 := ((aaaa − a) × (aa + aa)/(aa + a) − a)/a.
2035 := (aaaa − a)/(a + a + a) × aa/(a + a).
2036 := ((aaaa − a) × (aa + aa)/(aa + a) + a)/a.
2037 := (aaaaa + aaaa)/(a + a + a) × a/(a + a).
2038 := ((aaaa + a) × aa/(a + a) − a − a)/(a + a + a).
2039 := ((aaaa + a) × aa/(a + a) + a)/(a + a + a).
2040 := ((aaaa − a)/(a + a + a) × aa + aa − a)/(a + a).
2041 := ((aaaa − a)/(a + a + a) × aa + aa + a)/(a + a).
2042 := ((aaaa + a) × aa/(a + a) + aa − a)/(a + a + a).
2043 := (aaa/(a + a + a) × aaa − aa − aa + a)/(a + a).
2044 := (aaaa − aaa + aa + aa) × (a + a)/(a × a).
2044 := ((aaaa − aaa + aa + aa) × (a + a)/a + a)/a.
2046 := (aaaa − aaa + aa + aa + a) × (a + a)/(a × a).
2047 := (aaa − aa − aa) × (aa + aa + a)/(a × a).
2048 := (aaa/(a + a + a) × aaa − aa)/(a + a).
2049 := (aaa/(a + a + a) × aaa − aa + a + a)/(a + a).
2050 := ((aaa + a) × aaa/(aa + a) − aa) × (a + a)/(a × a).
2051 := (aaa/(a + a + a) × aaa − a)/(a + a) − (a + a)/a.
2052 := (aaa/(a + a + a) × aaa − a)/(a + a) − a/a.
2053 := (aaa/(a + a + a) × aaa − a)/(a + a).
2054 := (aaa/(a + a + a) × aaa + a)/(a + a).
2055 := (aaa/(a + a + a) × aaa + a + a + a)/(a + a).
2056 := ((aaaa + aa) × (aa + aa)/(aa + a) − a)/a.
2057 := (aaaa + aa) × aa/((a + a) × (a + a + a)).
2058 := (aaa − aa − a − a) × (aa + aa − a)/(a × a).
2059 := (aaa/(a + a + a) × aaa + aa)/(a + a).
2060 := (aaa/(a + a + a) × aaa + aa + a + a)/(a + a).
2061 := ((aaa + aaa) × (aaa + a)/(aa + a) − aa)/a.
2062 := ((aaa + aaa) × (aaa + a)/(aa + a) − aa + a)/a.
2063 := ((aaa+aaa+a)×aaa/(a+a+a)+a)/(a+a+a+a).
2064 := (aaa/(a + a + a) × aaa + a)/(a + a) + (aaa − a)/aa.
2065 := (aaa/(a + a + a) × aaa + aa + aa + a)/(a + a).
2066 := ((aaa + a) × aaa/(a + a + a) − aa − a)/(a + a).
2067 := ((aaa + a) × aaa/(a + a + a) − aa + a)/(a + a).
2068 := ((aaa + a) × aaa/(a + a) − aa − a)/(a + a + a).
2069 := ((aaa + a) × aaa/(a + a) − aa + a + a)/(a + a + a).
2070 := ((aaa × aaa + aa × aa)/(a + a) − aa)/(a + a + a).
2071 := (aa + aa − a − a − a) × (aaa − a − a)/(a × a).
2072 := (aaa + a) × aaa/((a + a + a) × (a + a)).
2073 := ((aaa + a) × aaa/(a + a + a) + a + a)/(a + a).
2074 := ((aaa + aaa) × (aaa + a)/(aa + a) + a + a)/a.
2075 := ((aaaa − aa − a − a) × (a + a) − aa × aa)/(a × a).
2076 := ((aaaa − a) × (a + a) − (aa + a) × (aa + a))/(a × a).
2077 := ((aaa + a) × aaa/(a + a + a) + aa − a)/(a + a).
2078 := ((aaa + a) × aaa/(a + a + a) + aa + a)/(a + a).
2079 := ((aaaa − aa) × (a + a) − aa × aa)/(a × a).
2080 := (((aaaa − aa) × (a + a) − aa × aa)/a + a)/a.
2081 := ((aaaa − aa + a) × (a + a) − aa × aa)/(a × a).
2082 := (((aaaa − aa + a) × (a + a) − aa × aa)/a + a)/a.
2083 := ((aaa + aaa) × (aaa + a)/(aa + a) + aa)/a.
2084 := ((aaa + aaa) × (aaa + a)/(aa + a) + aa + a)/a.
2085 := ((aaa + a + a) × aaa/(a + a + a) − aa)/(a + a).
2088 := ((aaa+a+a)×aaa/(a+a+a)−aa−a−a)/(a+a).
2087 := ((aaa + a) × (aaa + a)/(a + a) − aa)/(a + a + a).
2088 := (aaaa + aaaa − aaa − aa − aa − a)/a.
2089 := (aaaa + aaaa − aaa − aa − aa)/a.
2090 := (aaaa × (a + a) − (aa + a) × aa)/(a × a).
2091 := ((aaa + a + a) × aaa/(a + a + a) + a)/(a + a).
2092 := ((aaaa + a) × (a + a) − (aa + a) × aa)/(a × a).
2093 := (aaaa − aaa + a) × (aa + aa + a)/(aa × a).
2094 := ((aaaa + a + a) × (a + a) − (aa + a) × aa)/(a × a).
2095 := ((aaaa − a − a − a) × (a + a) − aa × aa)/(a × a).
2096 := (aaaa + aaaa − aaa − aa − a − a − a − a)/a.
2097 := (aaa + aaa + aa) × (aa − a − a)/(a × a).
2098 := (aaaa + aaaa − aaa − aa − a − a)/a.
2099 := (aaaa + aaaa − aaa − aa − a)/a.
2100 := (aa + aa − a) × (aaa − aa)/(a × a).
2101 := (aaaa × (a + a) − aa × aa)/(a × a).
2102 := (aaaa + aaaa − aaa − aa + a + a)/a.
2103 := ((aaaa + a) × (a + a) − aa × aa)/(a × a).
2104 := (((aaaa + a) × (a + a) − aa × aa)/a + a)/a.
2105 := (((aaaa + a) × (a + a) − aa × aa)/a + a + a)/a.
2106 := (aaa + aaa + aa + a) × (aa − a − a)/(a × a).
2107 := (aaaa + aaaa − aaa − a − a − a − a)/a.
2108 := (aaaa + aaaa − aaa − a − a − a)/a.
2109 := (aaaa + aaaa − aaa − a − a)/a.
2110 := (aaaa + aaaa − aaa − a)/a.
2111 := (aaaa + aaaa − aaa)/a.
2112 := (aaaa + aaaa − aaa + a)/a.
2113 := (aaaa + aaaa − aaa + a + a)/a.
2114 := (aaaa + aaaa − aaa + a + a + a)/a.
2115 := ((aaaa + a) × (a + a + a) − aaa × aa)/(a × a).
2116 := (((aaaa + a) × (a + a + a) − aaa × aa)/a + a)/a.
2117 := ((aa + aa − a) × aaaa/aa − a − a − a − a)/a.
2118 := ((aa + aa − a) × aaaa/aa − a − a − a)/a.
2119 := ((aa + aa − a) × aaaa/aa − a − a)/a.
2120 := ((aa + aa − a) × aaaa/aa − a)/a.
2121 := (aa + aa − a) × aaaa/(aa × a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2122 := (aaaa + aaaa − aaa + aa)/a.
2123 := (aaaa + aaaa − aaa + aa + a)/a.
2124 := (aaaa + aaaa − aaa + aa + a + a)/a.
2125 := (aaaa + aaaa − aaa + aa + a + a + a)/a.
2126 := ((aa + aa − a − a − a) × (aaa + a)/a − a − a)/a.
2127 := ((aa + aa − a − a − a) × (aaa + a)/a − a)/a.
2128 := (aa + aa − a − a − a) × (aaa + a)/(a × a).
2129 := ((aa + aa − a − a − a) × (aaa + a)/a + a)/a.
2130 := ((aa + aa − a − a − a) × (aaa + a)/a + a + a)/a.
2131 := ((aaaaa − a)/aa × (a + a) + aaa)/a.
2132 := ((aa + aa − a) × aaaa/aa + aa)/a.
2133 := (aaaa + aaaa − aaa + aa + aa)/a.
2134 := (aaaa + aaaa − aaa + aa + aa + a)/a.
2135 := (aaaa + aaaa − aaa + aa + aa + a + a)/a.
2136 := ((aaa + a) × aaa/(aa + a) + aaaa − aa)/a.
2137 := (aaaaaa/(aa + a + a) × a + a)/(a + a + a + a).
2138 := ((aaaa + aa) × (aa + aa − a)/aa − a − a − a − a)/a.
2139 := ((aaaa + aa) × (aa + aa − a)/aa − a − a − a)/a.
2140 := ((aaaa + aa) × (aa + aa − a)/aa − a − a)/a.
2141 := ((aaaa + aa) × (aa + aa − a)/aa − a)/a.
2142 := (aaaa + aa) × (aa + aa − a)/(aa × a).
2143 := ((aaaa + aa) × (aa + aa − a)/aa + a)/a.
2144 := ((aaaa + aa) × (aa + aa − a)/aa + a + a)/a.
2145 := ((aaaa + aa) × (aa + aa − a)/aa + a + a + a)/a.
2146 := ((aaa + a + a) × aaa/(a + a + a) + aaa)/(a + a).
2147 := (aa + aa − a − a − a) × (aaa + a + a)/(a × a).
2148 := ((aaa + a) × aaa/(aa + a) + aaaa + a)/a.
2149 := ((aaa + a) × aaa/(aa + a) + aaaa + a + a)/a.
2150 := ((aaa + a) × aaa/(aa + a) + aaaa + a + a + a)/a.
2151 := ((aaaa − aa − aa − aa − a − a) × (a + a)/a − a)/a.
2152 := (aaaa − aa − aa − aa − a − a) × (a + a)/(a × a).
2153 := ((aaaa + aa) × (aa + aa − a)/aa + aa)/a.
2154 := (aaaa − aa − aa − aa − a) × (a + a)/(a × a).
2155 := ((aaaa + aa + aa) × (aa + aa)/aa − aaa)/a.
2156 := (aaa − aa − a − a) × (aa + aa)/(a × a).
2157 := ((aaa − aa − a − a) × (aa + aa)/a + a)/a.
2158 := (aaaa − aa − aa − aa + a) × (a + a)/(a × a).
2159 := ((aaa + a) × aaa/(aa + a) + aaaa + aa + a)/a.
2160 := (aaa−a−a−a)×(aaaa−a)×(a+a)/(aaa×a×a).
2161 := ((aaaa−aa−a)×(aa+a)/(a+a)−aaa)/(a+a+a).
2162 := (aaaa + aaa) × (aa + aa + a)/((aa + a + a) × a).
2163 := (aaaa + aa + aa) × (aa + aa − a)/(aa × a).
2164 := ((aaaa + aa + aa) × (aa + aa − a)/aa + a)/a.
2165 := ((aaaa−aa+a)×(aa+a)/(a+a)−aaa)/(a+a+a).
2166 := ((aaaa−aaa)×(aa+a+a)/(a+a)−a−a)/(a+a+a).
2167 := ((aaaa − aa − aa) × (aa + aa)/aa − aa)/a.
2168 := ((aaaa − aa − aa) × (aa + aa)/aa − aa + a)/a.
2169 := ((aaaa − aa − aa) × (aa + aa)/aa − aa + a + a)/a.
2170 := (aaaaa − (aaa + aa) × aaa/(a + a))/(a + a).
2171 := ((aaaa − aa − aa − a − a) × (a + a)/a − a − a − a)/a.
2172 := ((aaaa − aa − aa − a − a) × (a + a)/a − a − a)/a.
2173 := ((aaaa − aa − aa − a − a) × (a + a)/a − a)/a.
2174 := (aaaa − aa − aa − a − a) × (a + a)/(a × a).
2175 := ((aaaa − aa − aa − a) × (aa + aa)/aa − a)/a.
2176 := (aaaa − aa − aa − a) × (a + a)/(a × a).
2177 := ((aaaa − aa − aa) × (aa + aa)/aa − a)/a.
2178 := (aaaa − aa − aa) × (a + a)/(a × a).
2179 := ((aaaa − aa − aa) × (aa + aa)/aa + a)/a.
2180 := (aaaa − aa − aa + a) × (a + a)/(a × a).
2181 := ((aaaa − aa − aa + a) × (a + a)/a + a)/a.
2182 := (aaaa − aa − aa + a + a) × (a + a)/(a × a).
2183 := ((aaa + aaa) × (aaa + a)/(aa + a) + aaa)/a.
2184 := (aa + a) × aaaaaa/(aaa × aa) × (a + a)/a.
2185 := (aaaa × (aa + a)/(a + a) − aaa)/(a + a + a).
19
2186 := (aaaa + aaaa − aa − aa − aa − a − a − a)/a.
2187 := ((aaaa + a) × (aa + a)/(a + a) − aaa)/(a + a + a).
2188 := (aaaa + aaaa − aa − aa − aa − a)/a.
2189 := (aaaa + aaaa − aa − aa − aa)/a.
2190 := (aaaa + aaaa − aa − aa − aa + a)/a.
2191 := (aaaa + aaaa − aa − aa − aa + a + a)/a.
2192 := (aaaa + aaaa − aa − aa − aa + a + a + a)/a.
2193 := ((aaaa − aa − a − a − a) × (a + a)/a − a)/a.
2194 := (aaaa − aa − a − a − a) × (a + a)/(a × a).
2195 := ((aaaa − aa − a − a − a) × (a + a)/a + a)/a.
2196 := (aaaa − aa − a − a) × (a + a)/(a × a).
2197 := ((aaaa − aa − a) × (a + a)/a − a)/a.
2198 := (aaaa − aa − a) × (a + a)/(a × a).
2199 := (aaaa + aaaa − aa − aa − a)/a.
2200 := (aaaa − aa) × (a + a)/(a × a).
2201 := (aaaa + aaaa − aa − aa + a)/a.
2202 := (aaaa − aa + a) × (a + a)/(a × a).
2203 := (aaaa + aaaa − aa − aa + a + a + a)/a.
2204 := (aaaa − aa + a + a) × (a + a)/(a × a).
2205 := ((aaaa − aa + a + a) × (a + a)/a + a)/a.
2206 := (aaaa + aaaa − aa − a − a − a − a − a)/a.
2207 := (aaaa + aaaa − aa − a − a − a − a)/a.
2208 := (aaaa + aaaa − aa − a − a − a)/a.
2209 := (aaaa + aaaa − aa − a − a)/a.
2210 := (aaaa + aaaa − aa − a)/a.
2211 := (aaaa + aaaa − aa)/a.
2212 := (aaaa + aaaa − aa + a)/a.
2213 := (aaaa + aaaa − aa + a + a)/a.
2214 := (aaaa + aaaa − aa + a + a + a)/a.
2215 := ((aaaa − a − a − a) × (a + a)/a − a)/a.
2216 := (aaaa − a − a − a) × (a + a)/(a × a).
2217 := ((aaaa − a − a − a) × (a + a)/a + a)/a.
2218 := (aaaa − a − a) × (a + a)/(a × a).
2219 := (aaaa + aaaa − a − a − a)/a.
2220 := (aaaa − a) × (a + a)/(a × a).
2221 := (aaaa + aaaa − a)/a.
2222 := aaaa × (a + a)/(a × a).
2223 := (aaaa + aaaa + a)/a.
2224 := (aaaa + a) × (a + a)/(a × a).
2225 := (aaaa + aaaa + a + a + a)/a.
2226 := (aaaa + a + a) × (a + a)/(a × a).
2227 := ((aaaa + a + a) × (a + a)/a + a)/a.
2228 := (aaaa + a + a + a) × (a + a)/(a × a).
2229 := ((aaaa + a + a + a) × (a + a)/a + a)/a.
2230 := (aaa + aaa + a) × (aa − a)/(a × a).
2231 := (aaaa + aaaa + aa − a − a)/a.
2232 := (aaaa + aaaa + aa − a)/a.
2233 := (aaaa + aaaa + aa)/a.
2234 := (aaaa + aaaa + aa + a)/a.
2235 := (aaaa + aaaa + aa + a + a)/a.
2236 := (aaaa + aaaa + aa + a + a + a)/a.
2237 := (aaaa + aaaa + aa + a + a + a + a)/a.
2238 := ((aaaa + aa − a − a) × (a + a)/a − a − a)/a.
2239 := ((aaaa + aa − a − a) × (a + a)/a − a)/a.
2240 := (aaaa + aa − a − a) × (a + a)/(a × a).
2241 := (aaaa + aaaa + aa + aa − a − a − a)/a.
2242 := (aaaa + aa − a) × (a + a)/(a × a).
2243 := (aaaa + aaaa + aa + aa − a)/a.
2244 := (aaaa + aa) × (a + a)/(a × a).
2245 := (aaaa + aaaa + aa + aa + a)/a.
2246 := (aaaa + aa + a) × (a + a)/(a × a).
2247 := ((aaaa + aa + a) × (a + a)/a + a)/a.
2248 := (aaaa + aa + a + a) × (a + a)/(a × a).
2249 := ((aaaa + aa + a + a) × (a + a)/a + a)/a.
20
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2250 := (aaaa + aa + a + a + a) × (a + a)/(a × a).
2251 := ((aaaa + aa + a + a + a) × (a + a)/a + a)/a.
2252 := ((aaaa + aa + a + a + a) × (a + a)/a + a + a)/a.
2253 := ((aaa + aa) × aaa/(a + a) − aa − a)/(a + a + a).
2254 := (aaaa + aaaa + aa + aa + aa − a)/a.
2255 := (aaaa + aaaa + aa + aa + aa)/a.
2256 := ((aaa + aa) × aaa/(a + a + a) − a − a)/(a + a).
2257 := (aaa + aa) × aaa/((a + a + a) × (a + a)).
2258 := ((aaa + aa) × aaa/(a + a + a) + a + a)/(a + a).
2259 := (aaaa × (aa + a)/(a + a) + aaa)/(a + a + a).
2260 := (aa + aa − a − a) × (aaa + a + a)/(a × a).
2261 := ((aaa + aa) × aaa/(a + a) + aa + a)/(a + a + a).
2262 := (aaaa + aa + aa − a − a) × (a + a)/(a × a).
2263 := ((aaa + aa) × aaa/(a + a + a) + aa + a)/(a + a).
2264 := (aaaa + aa + aa − a) × (a + a)/(a × a).
2265 := ((aaaa + aa + aa) × (aa + aa)/aa − a)/a.
2266 := (aaaa + aa + aa) × (a + a)/(a × a).
2267 := ((aaaa + aa + aa) × (aa + aa)/aa + a)/a.
2268 := (aaaa + aa + aa + a) × (a + a)/(a × a).
2269 := ((aaaa + aa + aa + a) × (aa + aa)/aa + a)/a.
2270 := (aaaa + aa + aa + a + a) × (a + a)/(a × a).
2271 := ((aaaa + aa + aa + a + a) × (a + a)/a + a)/a.
2272 := ((aaaa + aa + aa + a + a) × (a + a)/a + a + a)/a.
2273 := ((aaaaa − a) × (aa − a − a)/(aa + aa) + a)/(a + a).
2274 := ((aaa+aa)×(aaa+a)/(a+a)−aa+a)/(a+a+a).
2275 := (aa + aa + a + a + a) × aaaaaa/(aaa × aa).
2276 := ((aaaa + aa + aa) × (aa + aa)/aa + aa − a)/a.
2277 := (aaa − aa − a) × (aa + aa + a)/(a × a).
2278 := ((aaa − aa − a) × (aa + aa + a)/a + a)/a.
2279 := ((aaa − aa − a) × (aa + aa + a + a)/a + a)/a.
2280 := ((aaa − aa − a) × (aa + aa + a + a)/a + a + a)/a.
2281 := ((aaa + aa + a)/(a + a + a) × aaa + aa)/(a + a).
2282 := ((aaa+aa+a)/(a+a+a)×aaa+aa+a+a)/(a+a).
2283 := ((aaaa+aa+a)×(aa+a)/(a+a)+aaa)/(a+a+a).
2284 := ((aaaa+aa+aa+aa−a)×(aa+aa)/aa−a−a)/a.
2285 := ((aaaa + aa + aa + aa − a) × (aa + aa)/aa − a)/a.
2286 := (aaaa + aa + aa + aa − a) × (aa + aa)/(aa × a).
2287 := ((aaaa + aa + aa + aa) × (a + a)/a − a)/a.
2288 := (aaaa + aa + aa + aa) × (a + a)/(a × a).
2289 := (aa + aa − a) × (aaa − a − a)/(a × a).
2290 := ((aa + aa − a) × (aaa − a − a)/a + a)/a.
2291 := ((aa + aa − a) × (aaa − a − a)/a + a + a)/a.
2292 := (aaaa/aa × (a + a) − aa) × (aa + a)/(a × a).
2293 := ((aaaa/aa × (a + a) − aa) × (aa + a)/a + a)/a.
2294 := ((aaa + aa) × aaa/(a + a) + aaa)/(a + a + a).
2295 := ((aaa+aa+a)×(aaa+a)/(a+a+a)−a−a)/(a+a).
2296 := (aaa + aa + a) × (aaa + a)/((a + a + a) × (a + a)).
2297 := ((aaa + aaa − aa − a − a) × aa/a − a − a)/a.
2298 := ((aaa + aaa − aa − a − a) × aa/a − a)/a.
2299 := (aaa + aaa − aa − a − a) × aa/(a × a).
2300 := (aaa − aa) × (aa + aa + a)/(a × a).
2301 := ((aaa − aa) × (aa + aa + a)/a + a)/a.
2302 := ((aaa − aa) × (aa + aa + a)/a + a + a)/a.
2303 := ((aaa − aa) × (aa + aa + a)/a + a + a + a)/a.
2304 := (aaaa/aa × (a + a) − aa + a) × (aa + a)/(a × a).
2305 := ((aa + aa − a) × (aaa − a)/a − a − a − a − a − a)/a.
2306 := ((aa + aa − a) × (aaa − a)/a − a − a − a − a)/a.
2307 := ((aa + aa − a) × (aaa − a)/a − a − a − a)/a.
2308 := ((aa + aa − a) × (aaa − a)/a − a − a)/a.
2309 := ((aa + aa − a) × (aaa − a)/a − a)/a.
2310 := (aa + aa − a) × (aaa − a)/(a × a).
2311 := (aaaa + aaaa + aaa − aa − aa)/a.
2312 := (aaaa × (aa + a)/aa + aaaa − aa)/a.
2313 := ((aaaa + aaaa) × (aa + a)/aa − aaa)/a.
2314 := ((aaaa + aaaa) × (aa + a)/aa − aaa + a)/a.
2315 := (aaaaa + a) × (aa − a)/((aa + a) × (a + a + a + a)).
2316 := ((aaa + aaa − aa) × aa/a − a − a − a − a − a)/a.
2317 := ((aaa + aaa − aa) × aa/a − a − a − a − a)/a.
2318 := ((aaa + aaa − aa) × aa/a − a − a − a)/a.
2319 := ((aaa + aaa − aa) × aa/a − a − a)/a.
2320 := ((aaa + aaa − aa) × aa/a − a)/a.
2321 := (aaa + aaa − aa) × aa/(a × a).
2322 := (aaaa + aaaa + aaa − aa)/a.
2323 := (aa + aa + a) × aaaa/(aa × a).
2324 := ((aa + aa + a) × aaaa/aa + a)/a.
2325 := ((aa + aa + a) × aaaa/aa + a + a)/a.
2326 := ((aa + aa + a) × aaaa/aa + a + a + a)/a.
2327 := ((aa + aa − a) × aaa/a − a − a − a − a)/a.
2328 := ((aa + aa − a) × aaa/a − a − a − a)/a.
2329 := ((aa + aa − a) × aaa/a − a − a)/a.
2330 := ((aa + aa − a) × aaa/a − a)/a.
2331 := (aa + aa − a) × aaa/(a × a).
2332 := ((aa + aa − a) × aaa/a + a)/a.
2333 := (aaaa + aaaa + aaa)/a.
2334 := (aaaa + aaaa + aaa + a)/a.
2335 := (aaaa + aaaa + aaa + a + a)/a.
2336 := (aaaa + aaaa + aaa + a + a + a)/a.
2337 := (aaaa + aaaa + aaa + a + a + a + a)/a.
2338 := (aaaa + aaaa + aaa + a + a + a + a + a)/a.
2339 := ((aaa + aaa + aa + a) × (aa − a)/a − a)/a.
2340 := (aaa + aaa + aa + a) × (aa − a)/(a × a).
2341 := ((aaa + aaa + aa + a) × (aa − a)/a + a)/a.
2342 = (aaaa + aaaa + aaa + aa − a − a)/a.
2343 := (aaaa + aaaa + aaa + aa − a)/a.
2344 := (aaaa + aaaa + aaa + aa)/a.
2345 := ((aaaa + a) × (a + a) + aa × aa)/(a × a).
2346 := (aaaa + aa) × (aa + aa + a)/(aa × a).
2347 := ((aaaa + a + a) × (a + a) + aa × aa)/(a × a).
2348 := ((aaaa + aa) × (aa + aa + a)/aa + a + a)/a.
2349 := ((aa + aa − a) × (aaa + a)/a − a − a − a)/a.
2350 := ((aa + aa − a) × (aaa + a)/a − a − a)/a.
2351 := ((aa + aa − a) × (aaa + a)/a − a)/a.
2352 := (aa + aa − a) × (aaa + a)/(a × a).
2353 := ((aa + aa − a) × (aaa + a)/a + a)/a.
2354 := (aaaa + aaaa + aaa + aa + aa − a)/a.
2355 := (aaaa + aaaa + aaa + aa + aa)/a.
2356 := (aaaa + aaaa + aaa + aa + aa + a)/a.
2357 := ((aaaa + aa) × (aa + aa + a)/aa + aa)/a.
2358 := ((aaaa + aa) × (aa + aa + a)/aa + aa + a)/a.
2359 := ((aaaa + aa + a + a) × (aa + aa)/aa + aaa)/a.
2360 := (aaa + aaa + aa + a + a + a) × (aaa − a)/(aa × a).
2361 := (((aaaa + aa − a) × (a + a) + aa × aa)/a − a − a)/a.
2362 := (((aaaa + aa − a) × (a + a) + aa × aa)/a − a)/a.
2363 := ((aaaa + aa − a) × (a + a) + aa × aa)/(a × a).
2364 := (((aaaa + aa) × (a + a) + aa × aa)/a − a)/a.
2365 := ((aaaa + aa) × (a + a) + aa × aa)/(a × a).
2366 := (aaaa × (a + a) + (aa + a) × (aa + a))/(a × a).
2367 := ((aaaa + aa + a) × (a + a) + aa × aa)/(a × a).
2368 := ((aaaa + aa + aa) × (aa + aa + a)/aa − a)/a.
2369 := (aaaa + aa + aa) × (aa + aa + a)/(aa × a).
2370 := ((aaaa + aa + aa) × (aa + aa + a)/aa + a)/a.
2371 := ((aaa + a + a) × (aa + aa − a)/a − a − a)/a.
2372 := ((aaa + a + a) × (aa + aa − a)/a − a)/a.
2373 := (aaa + a + a) × (aa + aa − a)/(a × a).
2374 := ((aaa + a + a) × (aa + aa − a)/a + a)/a.
2375 := ((aaa − a − a − a) × (aa + aa)/a − a)/a.
2376 := (aaa − a − a − a) × (aa + aa)/(a × a).
2377 := ((aaa − a − a − a) × (aa + aa)/a + a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2378 := (aaaa + aaa − aa − aa − aa) × (a + a)/(a × a).
2379 := ((aaa − a − a − a) × (aa + aa)/a + a + a + a)/a.
2380 := ((aaa − a − a − a) × (aa + aa)/a + a + a + a + a)/a.
2381 := ((aaa + a + a) × (aa + aa − a)/a − a − a − a + aa)/a.
2382 := ((aaa + a + a) × (aa + aa − a)/a − a − a + aa)/a.
2383 := ((aaa + a + a) × (aa + aa − a)/a − a + aa)/a.
2384 := ((aaa + a + a) × (aa + aa − a)/a + aa)/a.
2385 := ((aaa + a + a) × (aa + aa − a)/a + aa + a)/a.
2386 := ((aaa − a − a) × (aa + aa)/a − aa − a)/a.
2387 := ((aaa − a − a) × (aa + aa)/a − aa)/a.
2388 := ((aaa − a − a) × (aa + aa)/a − aa + a)/a.
2389 := ((aaa − a − a) × (aa + aa)/a − aa + a + a)/a.
2390 := ((aaa − a − a) × (aa + aa)/a − aa + a + a + a)/a.
2391 = ((aaa + a + a + a) × (aa + aa − a)/a − a − a − a)/a.
2392 := ((aaa + a + a + a) × (aa + aa − a)/a − a − a)/a.
2393 := ((aaa + a + a + a) × (aa + aa − a)/a − a)/a.
2394 := (aaa + a + a + a) × (aa + aa − a)/(a × a).
2395 := ((aaa + a + a + a) × (aa + aa − a)/a + a)/a.
2396 := ((aaa − a − a) × (aa + aa)/a − a − a)/a.
2397 := ((aaa − a − a) × (aa + aa)/a − a)/a.
2398 := (aaa − a − a) × (aa + aa)/(a × a).
2399 := ((aaa − a − a) × (aa + aa)/a + a)/a.
2400 := (aa + aa + a + a) × (aaa − aa)/(a × a).
2401 := ((aa + aa + a + a) × (aaa − aa)/a + a)/a.
2402 := (aaaa × (aa + a)/aa − aa) × (a + a)/(a × a).
2403 := ((aaaa × (aa + a)/aa − aa) × (a + a)/a + a)/a.
2404 := ((aaaa × (aa + a)/aa − aa) × (a + a)/a + a + a)/a.
2405 := (aaaa − a) × (aa + a + a)/((a + a + a) × (a + a)).
2406 := ((aaaa−a)×aa/(a+a)+aaaa+a+a)/(a+a+a).
2407 := ((aaaa + aaa) × (aa + a)/(a + a) − aaa)/(a + a + a).
2408 := (aaaaa+a)/(a+a+a+a)−(aaaa−a)/(a+a+a).
2409 := ((aaaa + a) × (aa + a + a)/(a + a) − a)/(a + a + a).
2410 := ((aaaa+a)×(aa+a+a)/(a+a)+a+a)/(a+a+a).
2411 := ((aaaa + aaaa − aa) × (aa + a)/aa − a)/a.
2412 := (aaaa/aa × (a + a) − a) × (aa + a)/(a × a).
2413 := ((aaaa + aaaa) × (aa + a)/aa − aa)/a.
2414 := ((aaaa + aaaa) × (aa + a)/aa − aa + a)/a.
2415 := ((aaaa + aaaa) × (aa + a)/aa − aa + a + a)/a.
2416 := ((aa + aa) × (aaa − a)/a − a − a − a − a)/a.
2417 := ((aa + aa) × (aaa − a)/a − a − a − a)/a.
2418 := ((aa + aa) × (aaa − a)/a − a − a)/a.
2419 := ((aa + aa) × (aaa − a)/a − a)/a.
2420 := (aa + aa) × (aaa − a)/(a × a).
2421 := ((aa + aa) × (aaa − a)/a + a)/a.
2422 := (aaaa + aaa − aa) × (a + a)/(a × a).
2423 := ((aaaa + aaaa) × (aa + a)/aa − a)/a.
2424 := aaaa × (aa + a) × (a + a)/(aa × a × a).
2425 := ((aaaa + aaaa) × (aa + a)/aa + a)/a.
2426 := (aaaa × (aa + a)/aa + a) × (a + a)/(a × a).
2427 := ((aaaa × (aa + a)/aa + a) × (a + a)/a + a)/a.
2428 := ((aaaa × (aa + a)/aa + a) × (a + a)/a + a + a)/a.
2429 := ((aaa + aaa − a) × (aaa − a)/(aa − a) − a − a)/a.
2430 := ((aaa + aaa − a) × (aaa − a)/(aa − a) − a)/a.
2431 := (aaa + aaa − a) × (aaa − a)/((aa − a) × a).
2432 := ((aaa + aaa − a) × (aaa − a)/(aa − a) + a)/a.
2433 := (aaaa + aaaa + aaa + aaa − aa)/a.
2434 := ((aa + aa + a) × aaaa/aa + aaa)/a.
2435 := ((aaaa + aaaa) × (aa + a)/aa + aa)/a.
2436 := (aaaa/aa × (a + a) + a) × (aa + a)/(a × a).
2437 := ((aa + aa) × aaa/a − a − a − a − a − a)/a.
2438 := ((aa + aa) × aaa/a − a − a − a − a)/a.
2439 := ((aa + aa) × aaa/a − a − a − a)/a.
2440 := ((aa + aa) × aaa/a − a − a)/a.
2441 := ((aa + aa) × aaa/a − a)/a.
21
2442 := (aa + aa) × aaa/(a × a).
2443 := ((aa + aa) × aaa/a + a)/a.
2444 := (aaaa + aaa) × (a + a)/(a × a).
2445 := (aaaa + aaaa + aaa + aaa + a)/a.
2446 := (aaaa + aaa + a) × (a + a)/(a × a).
2447 := ((aaaa + aaa + a + a) × (a + a)/a − a)/a.
2448 := (aaaa + aaa + a + a) × (a + a)/(a × a).
2449 := ((aaaa + aaa + a + a) × (a + a)/a + a)/a.
2450 := ((aa + aa) × aaa/a + aa − a − a − a)/a.
2451 := ((aa + aa) × aaa/a + aa − a − a)/a.
2452 := ((aa + aa) × aaa/a + aa − a)/a.
2453 := ((aa + aa) × aaa/a + aa)/a.
2454 := ((aa + aa) × aaa/a + aa + a)/a.
2455 := ((aa + aa) × aaa/a + aa + a + a)/a.
2456 := ((aa + aa) × aaa/a + aa + a + a + a)/a.
2457 := ((aa + aa) × aaa/a + aa + a + a + a + a)/a.
2458 := ((aa + aa) × aaa/a + aa + a + a + a + a + a)/a.
2459 := ((aa + aa) × (aaa + a)/a − a − a − a − a − a)/a.
2460 := ((aa + aa) × (aaa + a)/a − a − a − a − a)/a.
2461 := ((aa + aa) × (aaa + a)/a − a − a − a)/a.
2462 := ((aa + aa) × (aaa + a)/a − a − a)/a.
2463 := ((aa + aa) × (aaa + a)/a − a)/a.
2464 := (aa + aa) × (aaa + a)/(a × a).
2465 := ((aa + aa) × (aaa + a)/a + a)/a.
2466 := ((aa + aa) × (aaa + a)/a + a + a)/a.
2467 := ((aa + aa) × (aaa + a)/a + a + a + a)/a.
2468 := (aaaa + aaa + aa + a) × (a + a)/(a × a).
2469 := ((aaaa + aaa + aa + a) × (a + a)/a + a)/a.
2470 := (aaaa + aaa + aa + a + a) × (a + a)/(a × a).
2471 := ((aaaa + aaa + aa + a + a) × (a + a)/a + a)/a.
2472 := ((aa + aa) × (aaa + a)/a + aa − a − a − a)/a.
2473 := ((aa + aa) × (aaa + a)/a + aa − a − a)/a.
2474 := ((aa + aa) × (aaa + a)/a + aa − a)/a.
2475 := ((aa + aa) × (aaa + a)/a + aa)/a.
2476 := ((aa + aa) × (aaa + a)/a + aa + a)/a.
2477 := ((aa + aa) × (aaa + a)/a + aa + a + a)/a.
2478 := ((aa + aa) × (aaa + a)/a + aa + a + a + a)/a.
2479 := (aaa × aaa/(aa − a − a) + aaaa − a)/a.
2480 := (aaa × aaa/(aa − a − a) + aaaa)/a.
2481 := (aaa × aaa/(aa − a − a) + aaaa + a)/a.
2482 := ((aaa + a + a) × (aa + aa)/a − a − a − a − a)/a.
2483 := ((aaa + a + a) × (aa + aa)/a − a − a − a)/a.
2484 := ((aaa + a + a) × (aa + aa)/a − a − a)/a.
2485 := ((aaa + a + a) × (aa + aa)/a − a)/a.
2486 := (aaa + a + a) × (aa + aa)/(a × a).
2487 := ((aaa + a + a) × (aa + aa)/a + a)/a.
2488 := (aaaa + aaa + aa + aa) × (a + a)/(a × a).
2489 := ((aaaa + aaa + aa + aa) × (a + a)/a + a)/a.
2490 := (aaaa + aaa + aa + aa + a) × (a + a)/(a × a).
2491 := (aaa × aaa/(aa − a − a) + aaaa + aa)/a.
2492 := (aaa − aa − aa) × (aaa + a)/((a + a + a + a) × a).
2493 := (a−aaaa+a+a)×(a−aa+a)/((a+a+a+a)×a).
2494 := (aaaaa + aaa + a)/(aa − a − a) × (a + a)/a.
2495 := (aaaaa − aaaa)/(a + a + a + a) − (aa − a)/(a + a).
2496 := ((aaaa − a) × aa/(a + a) − aaaa)/(a + a) − a/a.
2497 := ((aaaa − a) × aa/(a + a) − aaaa)/(a + a).
2498 := (aaaaa − aaaa)/(a + a + a + a) − (a + a)/a.
2499 := (aaaaa − aaaa)/(a + a + a + a) − a/a.
2500 := (aaaaa − aaaa)/(a + a + a + a).
2501 := ((aaaaa − aaaa)/(a + a) × a + a + a)/(a + a).
2502 := (aaaa + a) × (aa − a − a)/(a + a)/(a + a).
2503 := (aaaaa − aaaa + aa + a)/(a + a + a + a).
2504 := ((aaa − a − a) × (aa + aa + a)/a − a − a − a)/a.
2505 := ((aaa − a − a) × (aa + aa + a)/a − a − a)/a.
22
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2506 := ((aaa − a − a) × (aa + aa + a)/a − a)/a.
2507 := (aaa − a − a) × (aa + aa + a)/(a × a).
2508 := (aaa + a + a + a) × (aa + aa)/(a × a).
2509 := ((aaa + a + a + a) × (aa + aa)/a + a)/a.
2510 := ((aaa + a + a + a) × (aa + aa)/a + a + a)/a.
2511 := ((aaa + a + a + a) × (aa + aa)/a + a + a + a)/a.
2512 := ((aaa + a + a + a) × (aa + aa)/a + a + a + a + a)/a.
2514 := ((aa + aa + a + a + a) × aaaa/aa − aa − a)/a.
2514 := ((aa + aa + a + a + a) × aaaa/aa − aa)/a.
2515 := ((aa + aa + a + a + a) × aaaa/aa − aa + a)/a.
2516 := (aaa × aaa/(aa − a − a) − aaa) × (a + a)/(a × a).
2517 := ((aaa + aaa − aa − a) × (aa + a)/a − a − a − a)/a.
2518 := ((aaa + aaa − aa − a) × (aa + a)/a − a − a)/a.
2519 := ((aaa + aaa − aa − a) × (aa + a)/a − a)/a.
2520 := (aaa + aaa − aa − a) × (aa + a)/(a × a).
2521 := ((aaa + aaa − aa − a) × (aa + a)/a + a)/a.
2522 := ((aa + aa + a + a + a) × aaaa/aa − a − a − a)/a.
2523 := ((aa + aa + a + a + a) × aaaa/aa − a − a)/a.
2524 := ((aa + aa + a + a + a) × aaaa/aa − a)/a.
2525 := (aa + aa + a + a + a) × aaaa/(aa × a).
2526 := ((aa + aa + a + a + a) × aaaa/aa + a)/a.
2527 := ((aa + aa + a) × (aaa − a)/a − a − a − a)/a.
2528 := ((aa + aa + a) × (aaa − a)/a − a − a)/a.
2529 := ((aa + aa + a) × (aaa − a)/a − a)/a.
2530 := (aa + aa + a) × (aaa − a)/(a × a).
2531 := ((aa + aa + a) × (aaa − a)/a + a)/a.
2532 := (aaa + aaa − aa) × (aa + a)/(a × a).
2533 := ((aaa + aaa − aa) × (aa + a)/a + a)/a.
2534 := ((aaa + aaa − aa) × (aa + a)/a + a + a)/a.
2535 := ((aaa + aaa − aa) × (aa + a)/a + a + a + a)/a.
2536 := ((aaaa + aaaa) × (aa + a)/aa + aaa + a)/a.
2537 := ((aa + aa + a) × aaa/a − aa − a − a − a − a − a)/a.
2538 := ((aa + aa + a) × aaa/a − aa − a − a − a − a)/a.
2539 := ((aa + aa + a) × aaa/a − aa − a − a − a)/a.
2540 := ((aa + aa + a) × aaa/a − aa − a − a)/a.
2541 := ((aa + aa + a) × aaa/a − aa − a)/a.
2542 := ((aa + aa + a) × aaa/a − aa)/a.
2543 := ((aa + aa + a) × aaa/a − aa + a)/a.
2544 := ((aa + aa + a) × aaa/a − aa + a + a)/a.
2545 := ((aa + aa + a) × aaa/a − aa + a + a + a)/a.
2546 := ((aa + aa + a) × aaa/a − aa + a + a + a + a)/a.
2547 := ((aa + aa + a) × aaa/a − aa + a + a + a + a + a)/a.
2548 := ((aa + aa + a) × aaa/a − a − a − a − a − a)/a.
2549 := ((aa + aa + a) × aaa/a − a − a − a − a)/a.
2550 := ((aa + aa + a) × aaa/a − a − a − a)/a.
2551 := ((aa + aa + a) × aaa/a − a − a)/a.
2552 := ((aa + aa + a) × aaa/a − a)/a.
2553 := (aa + aa + a) × aaa/(a × a).
2554 := ((aa + aa + a) × aaa/a + a)/a.
2555 := ((aa + aa + a) × aaa/a + a + a)/a.
2556 := ((aa + aa + a) × aaa/a + a + a + a)/a.
2557 := ((aa + aa + a) × aaa/a + a + a + a + a)/a.
2558 := ((aa + aa + a) × aaa/a + a + a + a + a + a)/a.
2559 := ((aa + aa − a) × (aaa + aa)/a − a − a − a)/a.
2560 := ((aa + aa − a) × (aaa + aa)/a − a − a)/a.
2561 := ((aa + aa − a) × (aaa + aa)/a − a)/a.
2562 := (aa + aa − a) × (aaa + aa)/(a × a).
2563 := (aaa + aaa + aa) × aa/(a × a).
2564 := ((aaa + aaa + aa) × aa/a + a)/a.
2565 := ((aaa + aaa + aa) × aa/a + a + a)/a.
2566 := ((aaa + aaa + aa) × aa/a + a + a + a)/a.
2567 := ((aaa + aaa + aa) × aa/a + a + a + a + a)/a.
2568 := ((aaa + aaa + aa) × aa/a + a + a + a + a + a)/a.
2569 := ((aaa + aaa + aa) × aa/a + a + a + a + a + a + a)/a.
2570 := ((aaa + aaa + aa) × aa/a + aa − a − a − a − a)/a.
2571 := ((aaa + aaa + aa) × aa/a + aa − a − a − a)/a.
2572 := ((aaa + aaa + aa) × aa/a + aa − a − a)/a.
2573 := ((aaa + aaa + aa) × aa/a + aa − a)/a.
2574 := (aaa + aaa + aa + a) × aa/(a × a).
2575 := ((aa + aa + a) × (aaa + a)/a − a)/a.
2576 := (aa + aa + a) × (aaa + a)/(a × a).
2577 := ((aa + aa + a) × (aaa + a)/a + a)/a.
2578 := ((aa + aa + a) × (aaa + a)/a + a + a)/a.
2579 := ((aa + aa + a) × (aaa + a)/a + a + a + a)/a.
2580 := ((aa + aa + a) × (aaa + a)/a + a + a + a + a)/a.
2581 := ((aaa + aa + a) × (aa + aa − a)/a − a − a)/a.
2582 := ((aaa + aa + a) × (aa + aa − a)/a − a)/a.
2583 := (aaa + aa + a) × (aa + aa − a)/(a × a).
2584 := ((aaa + aa + a) × (aa + aa − a)/a + a)/a.
2585 := (aaa + aaa + aa + a + a) × aa/(a × a).
2586 := ((aaa + aaa + aa + a + a) × aa/a + a)/a.
2587 := ((aaa + aaa + aa + a + a) × aa/a + a + a)/a.
2588 := ((aaa + aaa + aa + a + a) × aa/a + a + a + a)/a.
2589 := ((aaa + aaa + aa + a + a) × aa/a + a + a + a + a)/a.
2590 := ((aa + aa + a + a) × (aaa − a − a − a)/a − a − a)/a.
2591 := ((aa + aa + a + a) × (aaa − a − a − a)/a − a)/a.
2592 := (aa + aa + a + a) × (aaa − a − a − a)/(a × a).
2593 := ((aa + aa + a + a) × (aaa − a − a − a)/a + a)/a.
2594 := ((aa + aa + a + a) × (aaa − a − a − a)/a + a + a)/a.
2595 := ((aaa + a + a) × (aa + aa + a)/a − a − a − a − a)/a.
2596 := ((aaa + a + a) × (aa + aa + a)/a − a − a − a)/a.
2597 := ((aaa + a + a) × (aa + aa + a)/a − a − a)/a.
2599 := ((aaa + a + a) × (aa + aa + a)/a − a)/a.
2599 := (aaa + a + a) × (aa + aa + a)/(a × a).
2600 := ((aaa + a + a) × (aa + aa + a)/a + a)/a.
2601 := ((aaa + a + a) × (aa + aa + a)/a + a + a)/a.
2602 := ((aaa + a + a) × (aa + aa + a)/a + a + a + a)/a.
2603 := ((aaa + aa + a + a) × (aa + aa − a)/a − a)/a.
2604 := (aaa + aa + a + a) × (aa + aa − a)/(a × a).
2605 := ((aaa + aa + a + a) × (aa + aa − a)/a + a)/a.
2606 := ((aaa + aa + a + a) × (aa + aa − a)/a + a + a)/a.
2607 := ((aaa + aa + a + a) × (aa + aa − a)/a + a + a + a)/a.
2608 := ((aaa + a) × aaa/(a + a) − aaaa + aaa)/(a + a).
2609 := (aaa/(a + a + a) × aaa + aaaa)/(a + a).
2610 := (aaa/(a + a + a) × aaa + aaaa + a + a)/(a + a).
2611 := (aaaaa−aaa×(aa+a)/(a+a)−a)/(a+a+a+a).
2612 := ((aaaa + aaaa − aa) × (aa + a + a)/aa − a)/a.
2613 := (aaaa/aa × (a + a) − a) × (aa + a + a)/(a × a).
2614 := ((aaaa + aaaa − aa) × (aa + a + a)/aa + a)/a.
2615 := ((aaaa + aaaa) × (aa + a + a)/aa − aa)/a.
2616 := (aa + aa + a + a) × (aaa − a − a)/(a × a).
2617 := ((aa + aa + a + a) × (aaa − a − a)/a + a)/a.
2618 := ((aa + aa + a + a) × (aaa − a − a)/a + a + a)/a.
2619 := ((aaa + a + a + a) × (aa + aa + a)/a − a − a − a)/a.
2620 := ((aaa + a + a + a) × (aa + aa + a)/a − a − a)/a.
2621 := ((aaa + a + a + a) × (aa + aa + a)/a − a)/a.
2622 := (aaa + a + a + a) × (aa + aa + a)/(a × a).
2623 := ((aaa + a + a + a) × (aa + aa + a)/a + a)/a.
2624 := (aaaa × (aa + a + a)/aa − a) × (a + a)/(a × a).
2625 := ((aaaa + aaaa) × (aa + a + a)/aa − a)/a.
2626 := aaaa × (aa + a + a)/aa × (a + a)/(a × a).
2627 := ((aaaa + aaaa) × (aa + a + a)/aa + a)/a.
2628 := ((aa + aa + a + a) × (aaa − a − a)/a + aa + a)/a.
2629 := ((aa + aa + a + a) × (aaa − a − a)/a + aa + a + a)/a.
2630 := ((aa+aa+a+a)×(aaa−a−a)/a+aa+a+a+a)/a.
2631 := ((aaa + a + a + a) × (aa + aa + a)/a + aa − a − a)/a.
2632 := (aaa + aaa + aa + a + a) × (aaa + a)/((aa − a) × a).
2633 := ((aaa + a) × aaa/(a + a + a) + aaaa + aa)/(a + a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2634 := (aaaa − aaa − aaa − aa) × (a + a + a)/(a × a).
2635 := ((aa + aa + a + a + a) × aaaa/aa + aaa − a)/a.
2636 := ((aa + aa + a + a + a) × aaaa/aa + aaa)/a.
2637 := ((aaaa + aaaa) × (aa + a + a)/aa + aa)/a.
2638 := ((aaaa + aaaa + aa) × (aa + a + a)/aa − a)/a.
2639 := (aaaa + aaaa + aa) × (aa + a + a)/(aa × a).
2640 := ((aaaa + aaaa + aa) × (aa + a + a)/aa + a)/a.
2641 := ((aaaa + aaa + aaa − aa) × (a + a)/a − a − a − a)/a.
2642 := ((aaaa + aaa + aaa − aa) × (a + a)/a − a − a)/a.
2643 := ((aaaa + aaa + aaa − aa) × (a + a)/a − a)/a.
2644 := (aaaa + aaa + aaa − aa) × (a + a)/(a × a).
2645 := (aaaaaa/(aa + aa − a) × a − a)/(a + a).
2646 := (aaaaaa/(aa + aa − a) × a + a)/(a + a).
2647 := ((aaa + aaa − a) × (aa + a)/a − a − a − a − a − a)/a.
2648 := ((aaa + aaa − a) × (aa + a)/a − a − a − a − a)/a.
2649 := ((aaa + aaa − a) × (aa + a)/a − a − a − a)/a.
2650 := ((aaa + aaa − a) × (aa + a)/a − a − a)/a.
2651 := ((aaa + aaa − a) × (aa + a)/a − a)/a.
2652 := (aaa + aaa − a) × (aa + a)/(a × a).
2653 := ((aaa + aaa − a) × (aa + a)/a + a)/a.
2654 := ((aaa + aaa − a) × (aa + a)/a + a + a)/a.
2655 := ((aaa + aaa − a) × (aa + a)/a + a + a + a)/a.
2656 := ((aaa + aaa − a) × (aa + a)/a + a + a + a + a)/a.
2657 := ((aa + aa) × aa × aa/(a × a) − a − a − a − a − a)/a.
2658 := ((aa + aa) × aa × aa/(a × a) − a − a − a − a)/a.
2659 := ((aa + aa) × aa × aa/(a × a) − a − a − a)/a.
2660 := ((aa + aa) × aa × aa/(a × a) − a − a)/a.
2661 := ((aa + aa) × aa × aa/(a × a) − a)/a.
2662 := (aa + aa) × aa × aa/(a × a × a).
2663 := ((aa + aa) × aa × aa/(a × a) + a)/a.
2664 := (aaa + aaa) × (aa + a)/(a × a).
2665 := ((aaa + aaa) × (aa + a)/a + a)/a.
2666 := (aaaa + aaa + aaa) × (a + a)/(a × a).
2667 := ((aaaa + aaa + aaa) × (aa + aa)/aa + a)/a.
2668 := (aaaa + aaa + aaa + a) × (a + a)/(a × a).
2669 := (aaaaaa × (aa − a − a − a)/aaa − a)/(a + a + a).
2670 := (aaaa + aaa + aaa + a + a) × (a + a)/(a × a).
2671 := ((aaa + aaa + aa + aa − a) × aa/a − a − a)/a.
2672 := ((aaa + aaa + aa + aa − a) × aa/a − a)/a.
2673 := (aaa + aaa + aa + aa − a) × aa/(a × a).
2674 := ((aaa + aaa + a) × (aa + a)/a − a − a)/a.
2675 := ((aaa + aaa + a) × (aa + a)/a − a)/a.
2676 := (aaa + aaa + a) × (aa + a)/(a × a).
2677 := ((aaa + aaa + a) × (aa + a)/a + a)/a.
2678 := ((aaa + aaa + a) × (aa + a)/a + a + a)/a.
2679 := ((aaa + aaa + a) × (aa + a)/a + a + a + a)/a.
2680 := ((aaa + aa) × (aa + aa)/a − a − a − a − a)/a.
2681 := ((aaa + aa) × (aa + aa)/a − a − a − a)/a.
2682 := ((aaa + aa) × (aa + aa)/a − a − a)/a.
2683 := ((aaa + aa) × (aa + aa)/a − a)/a.
2684 := (aaa + aa) × (aa + aa)/(a × a).
2685 := ((aaa + aa) × (aa + aa)/a + a)/a.
2686 := ((aaa + aa) × (aa + aa)/a + a + a)/a.
2687 := ((aa + aa + a + a) × (aaa + a)/a − a)/a.
2688 := (aa + aa + a + a) × (aaa + a)/(a × a).
2689 := ((aa + aa + a + a) × (aaa + a)/a + a)/a.
2690 := ((aa + aa + a + a) × (aaa + a)/a + a + a)/a.
2691 := ((aa + aa + a + a) × (aaa + a)/a + a + a + a)/a.
2692 := ((aa + aa + a + a) × (aaa + a)/a + a + a + a + a)/a.
2693 := ((a − aaaaa) × (a − aa + a + a)/aa − a)/(a + a + a).
2694 := (aaaaa + a)/(a + a + a) + (a − aaaaa)/aa.
2695 := (aaa + aaa + aa + aa + a) × aa/(a × a).
2696 := ((aaa + aaa + aa + aa + a) × aa/a + a)/a.
2697 := ((aaa + aaa + aa + aa + a) × aa/a + a + a)/a.
23
2698 := ((aaa + aaa + aa + aa + a) × aa/a + a + a + a)/a.
2699 := ((aaa + aaa + a + a + a) × (aa + a)/a − a)/a.
2700 := (aaa + aaa + a + a + a) × (aa + a)/(a × a).
2701 := ((aaa + aaa + a + a + a) × (aa + a)/a + a)/a.
2702 := ((aaa + aaa + a + a + a) × (aa + a)/a + a + a)/a.
2703 := ((aaa + aa + a) × (aa + aa)/a − a − a − a)/a.
2704 := ((aaa + aa + a) × (aa + aa)/a − a − a)/a.
2705 := ((aaa + aa + a) × (aa + aa)/a − a)/a.
2706 := (aaa + aa + a) × (aa + aa)/(a × a).
2707 := ((aaa + aa + a) × (aa + aa)/a + a)/a.
2708 := ((aaa + aa + a) × (aa + aa)/a + a + a)/a.
2709 := ((aa + aa + a + a) × (aaa + a + a)/a − a − a − a)/a.
2710 := ((aa + aa + a + a) × (aaa + a + a)/a − a − a)/a.
2711 := ((aa + aa + a + a) × (aaa + a + a)/a − a)/a.
2712 := (aa + aa + a + a) × (aaa + a + a)/(a × a).
2713 := ((aa + aa + a + a) × (aaa + a + a)/a + a)/a.
2714 := ((aa + aa + a + a) × (aaa + a + a)/a + a + a)/a.
2715 := ((aaaaa + aaaa)/(aa − a − a) × (a + a) − a)/a.
2716 := (aaaaa + aaaa)/(aa − a − a) × (a + a)/a.
2717 := (aaaa + aaaa + a)/(a + a + a) × aa/(a + a + a).
2718 := (((aaa+a+a)×(aa+aa+a)+aa×aa)/a−a−a)/a.
2719 := (((aaa + a + a) × (aa + aa + a) + aa × aa)/a − a)/a.
2720 := ((aaa + a + a) × (aa + aa + a) + aa × aa)/(a × a).
2721 := ((aaaa+a+a)×(aa+aa)/(a+a+a)+a)/(a+a+a).
2722 := (aaaaa − aaa − aaa − a)/(a + a + a + a).
2723 := (aaaaa + a)/(a + a + a + a) − (aaa − a)/(a + a).
2724 := (aaaaa − aaaa − aa − a) × (a + a + a)/(aa × a).
2725 := (aa + aa + a + a + a) × (aaa − a − a)/(a × a).
2726 := ((aaa + aa + a + a) × (aa + aa)/a − a − a)/a.
2727 := ((aaa + aa + a + a) × (aa + aa)/a − a)/a.
2728 := (aaa + aa + a + a) × (aa + aa)/(a × a).
2729 := ((aaa + aa + a + a) × (aa + aa)/a + a)/a.
2730 := (aaa + aaa − aa − a) × (aa + a + a)/(a × a).
2731 := ((aaa + aaa − aa − a) × (aa + a + a)/a + a)/a.
2732 := ((aaa + aaa − aa − a) × (aa + a + a)/a + a + a)/a.
2733 := ((aaa+aaa−aa−a)×(aa+a+a)/a+a+a+a)/a.
2734 := ((aaa+aaa)/(a+a+a)×aaa−aa−a)/(a+a+a).
2735 := ((aaa + aaa) × aaa/(aa − a − a) − a − a − a)/a.
2736 := ((aaa × aaa)/(aa − a − a) − a) × (a + a)/(a × a).
2737 := ((aaa + aaa) × aaa/(aa − a − a) − a)/a.
2738 := (aaa + aaa) × aaa/((aa − a − a) × a).
2739 := ((aaa + aaa) × aaa/(aa − a − a) + a)/a.
2740 := ((aaa + aaa) × aaa/(aa − a − a) + a + a)/a.
2741 := (aaaaa + a)/(a + a + a + a) − aaa/(a + a + a).
2742 := ((aaa + aaa − aa) × (aa + a + a)/a − a)/a.
2743 := (aaa + aaa − aa) × (aa + a + a)/(a × a).
2744 := ((aaa + aaa − aa) × (aa + a + a)/a + a)/a.
2745 := ((aaa + aaa − aa) × (aa + a + a)/a + a + a)/a.
2746 := ((aaa + aaa − aa) × (aa + a + a)/a + a + a + a)/a.
2747 := (aaaaa − aaa − aa − a)/(a + a + a + a).
2748 := (aaaaa − aaa)/(a + a + a + a) − (a + a)/a.
2749 := (aaaaa − aaa)/(a + a + a + a) − a/a.
2750 := (aaaaa − aaa)/(a + a + a + a).
2751 := (aaaaa − aaa)/(a + a + a + a) + a/a.
2752 := (aaaaa − aaa)/(a + a + a + a) + (a + a)/a.
2753 := (aaaaa − aaa + aa + a)/(a + a + a + a).
2754 := ((aaaaaa + aa) × (a + a + a)/aa − aa − a)/aa.
2755 := (aaaaaa × (a + a + a)/aa + a + a)/aa.
2756 := (aaaaaa × (a + a + a)/aa + a + a)/aa + a/a.
2757 := (aaaaaa × (a + a + a)/aa + a + a)/aa + (a + a)/a.
2758 := (aaaaa − aaa)/(a + a + a + a) + (aa − a − a − a)/a.
2759 := (aaaaa − aaa)/(a + a + a + a) + (aa − a − a)/a.
2760 := (aaaaa − aaa)/(a + a + a + a) + (aa − a)/a.
2761 := (aaaaa − aaa)/(a + a + a + a) + aa/a.
24
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2762 := (aaaaa − aaa)/(a + a + a + a) + (aa + a)/a.
2763 := (aaaaa − aaa)/(a + a + a + a) + (aa + a + a)/a.
2764 := (aaaaa − aaa)/(a + a + a + a) + (aa + a + a + a)/a.
2765 := (aaaaa−aaa)/(a+a+a+a)+(aa+a+a+a+a)/a.
2766 := ((aaaaa + a) × (a + a + a)/(aa + a) − aa − a)/a.
2767 := ((aaaaa + a) × (a + a + a)/(aa + a) − aa)/a.
2768 := (aaaaa + a)/(a + a + a + a) − (aaa − a)/aa.
2769 := (aaaaa − aa − aa − aa − a − a)/(a + a + a + a).
2770 := (aaaaa − aa − aa − a)/(a + a + a + a) − (a + a)/a.
2771 := (aaaaa − aa − aa − a)/(a + a + a + a) − a/a.
2772 := (aaaaa − aa − aa − a)/(a + a + a + a).
2773 := (aaaaa − aa)/(a + a + a + a) − (a + a)/a.
2774 := (aaaaa − aa)/(a + a + a + a) − a/a.
2775 := (aaaaa − aa)/(a + a + a + a).
2776 := (aaaaa + a)/(a + a + a + a) − (a + a)/a.
2777 := (aaaaa + a)/(a + a + a + a) − a/a.
2778 := (aaaaa + a)/(a + a + a + a).
2779 := (aaaaa + a)/(a + a + a + a) + a/a.
2780 := (aaaa + a)/(a + a) × (aa − a)/(a + a).
2781 := ((aaaaa + aa)/(a + a) × a + a)/(a + a).
2782 := ((aaaaa + aa)/(a + a) × a + a)/(a + a) + a/a.
2783 := (aaaaa + aa + aa − a)/(a + a + a + a).
2784 := (aaa + aaa + aa − a) × (aa + a)/(a × a).
2785 := ((aaa + aaa + aa − a) × (aa + a)/a + a)/a.
2786 := (aaaaa + aa + aa + aa)/(a + a + a + a).
2787 := (aaaaa + aa + aa + aa)/(a + a + a + a) + a/a.
2788 := (aaaaa + a)/(a + a + a + a) + (aaa − a)/aa.
2789 := (aaaaa + a)/(a + a + a + a) + aa/a.
2790 := (aaaaa + a)/(a + a + a + a) + (aa + a)/a.
2791 := (aaaaa + a)/(a + a + a + a) + (aa + a + a)/a.
2792 := (aaaaa + a)/(a + a + a + a) + (aa + a + a + a)/a.
2793 := ((aaa + aaa + aa) × (aa + a)/a − a − a − a)/a.
2794 := ((aaa + aaa + aa) × (aa + a)/a − a − a)/a.
2795 := ((aaa + aaa + aa) × (aa + a)/a − a)/a.
2796 := (aaa + aaa + aa) × (aa + a)/(a × a).
2797 := ((aaa + aaa + aa) × (aa + a)/a + a)/a.
2798 := ((aaa + aaa + aa) × (aa + a)/a + a + a)/a.
2798 := ((aaa + aaa + aa) × (aa + a)/a + a + a + a)/a.
2800 := (aaa − aa) × (aaa + a)/((a + a) × (a + a)).
2801 := ((aaa − aa) × (aaa + a)/(a + a) + a + a)/(a + a).
2802 := ((aaaa + aa − a) × (aa − a)/(a + a) − a)/(a + a).
2803 := ((aaaa × aaa)/aa + a)/(a + a + a + a).
2804 := ((aaa + aa) × (aa + aa + a)/a − a − a)/a.
2805 := ((aaa + aa) × (aa + aa + a)/a − a)/a.
2806 := (aaa + aa) × (aa + aa + a)/(a × a).
2807 := ((aaa + aa) × (aa + aa + a)/a + a)/a.
2808 := (aaa + aaa + aa + a) × (aa + a)/(a × a).
2809 := ((aaa + aaa + aa + a) × (aa + a)/a + a)/a.
2810 := ((aaa + aaa + aa + a) × (aa + a)/a + a + a)/a.
2811 := (aaaaa + aaa + aa + aa)/(a + a + a + a).
2812 := ((aaa + aa + aa + a) × (aa + aa − a)/a − a − a)/a.
2813 := ((aaa + aa + aa + a) × (aa + aa − a)/a − a)/a.
2814 := (aaa + aa + aa + a) × (aa + aa − a)/(a × a).
2815 := (aaaaa + a)/(a + a + a + a) + aaa/(a + a + a).
2816 := ((aaa + aa + aa + a) × (aa + aa − a)/a + a + a)/a.
2817 := ((aaa + a) × aaaa/(aa + aa) − aa − aa)/(a + a).
2818 := ((aaa + aaa + aa + a + a) × (aa + a)/a − a − a)/a.
2819 := ((aaa + aaa + aa + a + a) × (aa + a)/a − a)/a.
2820 := (aaa + aaa + aa + a + a) × (aa + a)/(a × a).
2821 := ((aaa + aaa + aa + a + a) × (aa + a)/a + a)/a.
2822 := ((aaa + a) × aaaa/(aa + aa) − aa − a)/(a + a).
2823 := ((aaa + a) × aaaa/(aa + aa) − aa + a)/(a + a).
2824 := ((aaa + a + a) × (aaa − aa)/(a + a) − a − a)/(a + a).
2825 := (aaa + a + a) × (aaa − aa)/((a + a) × (a + a)).
2826 := ((aaa + a + a) × (aaa − aa)/(a + a) + a + a)/(a + a).
2827 := ((aaa + a) × aaaa/(aa + aa) − a − a)/(a + a).
2828 := (aaa + a) × aaaa/((aa + aa) × (a + a)).
2829 := (aaa + aa + a) × (aa + aa + a)/(a × a).
2830 := ((aaaa + aa)/(aa + aa) × aaa − a)/(a + a).
2831 := ((aaaa + aa)/(aa + aa) × aaa + a)/(a + a).
2832 := (aaa + aaa + aa + a + a + a) × (aa + a)/(a × a).
2833 := (aaaaa + aaa + aaa − a)/(a + a + a + a).
2834 := (aaaaa + a)/(a + a + a + a) + (aaa + a)/(a + a).
2835 := (aaa + aa + aa + a + a) × (aa + aa − a)/(a × a).
2836 := ((aaaa + aa)/(aa + aa) × aaa + aa)/(a + a).
2837 := ((aaaa−a)×(aa+aa+a)/(a+a+a)+a)/(a+a+a).
2838 := (aaa × aaa/(aa − a − a) − aaaa) × aa/(a × a).
2839 := (aaaaa + a)/(a + a + a + a) + (aaa + aa)/(a + a).
2840 := ((aaaa+aaaa+aa)×(aa+a+a+a)/aa−a−a)/a.
2841 := ((aaaa + aaaa + aa) × (aa + a + a + a)/aa − a)/a.
2842 := (aaaa + aaaa + aa) × (aa + a + a + a)/(aa × a).
2843 := ((aaaa + aaaa + aa) × (aa + a + a + a)/aa + a)/a.
2844 := ((aaa+aaa−a−a−a)×(aa+a+a)/a−a−a−a)/a.
2845 := ((aaa + aaa − a − a − a) × (aa + a + a)/a − a − a)/a.
2846 := ((aaa + aaa − a − a − a) × (aa + a + a)/a − a)/a.
2847 := (aaa + aaa − a − a − a) × (aa + a + a)/(a × a).
2848 := (aaa − aa − aa) × (aa + aa + aa − a)/(a × a).
2849 := aaaaaa/(aa + a + a) × a/(a + a + a).
2850 := (aaa + a + a + a) × (aaa − aa)/((a + a + a + a) × a).
2851 := (aaaaa − aaa)/(a + a + a + a) + aaaa/aa.
2852 := (aaa + aa + a + a) × (aa + aa + a)/(a × a).
2853 := ((aaa + a + a) × aaaa/aa − a)/(a + a + a + a).
2854 := ((aaa+a+a)×aaaa/aa+a+a+a)/(a+a+a+a).
2855 := ((aaa − aa) × (aaa + a)/(a + a) + aaa − a)/(a + a).
2856 := (aaaa + aa)/(aa + aa) × (aaa + a)/(a + a).
2857 := ((aaaa + aa)/(aa + aa) × (aaa + a) + a + a)/(a + a).
2858 := ((aaa−aa−aa−aa)×(aaa−a)/(a+a+a)−a−a)/a.
2859 := ((aaa−aa−aa−aa)×(aaa−a)/(a+a+a)−a)/a.
2860 := (aaa − aa − aa − aa) × (aaa − a)/((a + a + a) × a).
2861 := ((aaaaa − aaa) × (a + a + a)/(aa + a) + aaa)/a.
2862 := ((aaa + aaa − a) × (aa + a + a)/a − aa)/a.
2863 := ((aaa + aaa − a) × (aa + a + a)/a − aa + a)/a.
2864 := ((aaa + aaa − a) × (aa + a + a)/a − aa + a + a)/a.
2865 := ((aaa+aaa−a)×(aa+a+a)/a−aa+a+a+a)/a.
2876 := ((aaa+aaa−a)×(aa+a+a)/a−aa+a+a+a+a)/a.
2867 := (aaaa + aa)/(aa + aa) × (aaa + a)/(a + a) + aa/a.
2868 := ((aaa+aaa−a)×(aa+a+a)/a−a−a−a−a−a)/a.
2869 := ((aaa + aaa − a) × (aa + a + a)/a − a − a − a − a)/a.
2870 := ((aaa + aaa − a) × (aa + a + a)/a − a − a − a)/a.
2871 := ((aaa + aaa − a) × (aa + a + a)/a − a − a)/a.
2872 := ((aaa + aaa − a) × (aa + a + a)/a − a)/a.
2873 := (aaa + aaa − a) × (aa + a + a)/(a × a).
2874 := ((aaa + aaa) × (aa + a + a)/a − aa − a)/a.
2875 := ((aaa + aaa) × (aa + a + a)/a − aa)/a.
2876 := ((aaa + aaa) × (aa + a + a)/a − aa + a)/a.
2877 := ((aaa + aaa) × (aa + a + a)/a − aa + a + a)/a.
2878 := ((aaa + a + a + a) × aaaa/(aa + aa) − a)/(a + a).
2879 := ((aaaa − aaa) × (a + a + a) − aa × aa)/(a × a).
2880 := (aaaaa + a)/(a + a + a + a) + (aaaa + aa)/aa.
2881 := (aaaaaa × (a + a + a)/aaa − aaa − aa)/a.
2882 := ((aaa + aaa) × (aa + a + a)/a − a − a − a − a)/a.
2883 := ((aaa + aaa) × (aa + a + a)/a − a − a − a)/a.
2884 := ((aaa + aaa) × (aa + a + a)/a − a − a)/a.
2885 := ((aaa + aaa) × (aa + a + a)/a − a)/a.
2886 := (aaa + aaa) × (aa + a + a)/(a × a).
2887 := ((aaa + aaa) × (aa + a + a)/a + a)/a.
2888 := ((aaa + aaa) × (aa + a + a)/a + a + a)/a.
2889 := ((aaa + aaa) × (aa + a + a)/a + a + a + a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
2890 := (aaaa + aaa + aaa + aaa + a) × (a + a)/(a × a).
2891 := (aaaaaa × (a + a + a)/aaa − aaa − a)/a.
2892 := (aaaaaa × (a + a + a)/aaa − aaa)/a.
2893 := (aaaaaa × (a + a + a)/aaa − aaa + a)/a.
2894 := ((aaa + aaa) × (aa + a + a)/a + aa − a − a − a)/a.
2895 := ((aaa + aaa) × (aa + a + a)/a + aa − a − a)/a.
2896 := ((aaa + aaa) × (aa + a + a)/a + aa − a)/a.
2897 := ((aaa + aaa) × (aa + a + a)/a + aa)/a.
2898 := ((aaa + aaa + a) × (aa + a + a)/a − a)/a.
2899 := (aaa + aaa + a) × (aa + a + a)/(a × a).
2900 := ((aaa + aaa + a) × (aa + a + a)/a + a)/a.
2901 := ((aaa + aaa + a) × (aa + a + a)/a + a + a)/a.
2902 := ((aaa + aaa + a) × (aa + a + a)/a + a + a + a)/a.
2903 := ((aaa + aaa + a) × (aa + a + a)/a + a + a + a + a)/a.
2904 := (aa−aaa+aa+a)×(aa−aaa+a)/((a+a+a)×a).
2905 := ((aaaa − aa − a) × aaa/(aa + aa − a) + a)/(a + a).
2906 := ((aaa + aaa) × (aa + a + a)/a + aa + aa − a − a)/a.
2907 := (aaa+a+a+a)×(aaaa+aa)/(aa×(a+a+a+a)).
2908 := ((aaa + aaa) × (aa + a + a)/a + aa + aa)/a.
2909 := ((aaa + aaa) × (aa + a + a)/a + aa + aa + a)/a.
2910 := ((aaaaa − a − a)/(aa + aa − a) × aa + a)/(a + a).
2911 := ((aa+aa)×(aaa+a)×(aa+a+a)/(aa×a)−a)/a.
2912 := (aa + aa) × (aaa + a) × (aa + a + a)/(aa × a × a).
2913 := ((aaaaa + aa)/(a + a) × aa + a + a)/(aa + aa − a).
2914 := ((aaaa − aa) × aa/(a + a) − aaa − aaa)/(a + a).
2915 := (aaaa + a + a) × (aaa − a)/(a + a)/(aa + aa − a).
2916 := ((aaaaa − a) × (a + a + a)/aa − aaa − a − a − a)/a.
2917 := ((aaaaa − a) × (a + a + a)/aa − aaa − a − a)/a.
2918 := ((aaaaa − a) × (a + a + a)/aa − aaa − a)/a.
2919 := ((aaaaa − a) × (a + a + a)/aa − aaa)/a.
2920 := ((aaaaa − a) × (a + a + a)/aa − aaa + a)/a.
2921 := ((aaaaa − a) × (a + a + a)/aa − aaa + a + a)/a.
2922 := ((aaaaa − a) × (a + a + a)/aa − aaa + a + a + a)/a.
2923 := ((aaa + aa + aa) × (aa + aa)/a − a − a − a)/a.
2924 := (aaaaaa + a)/((aaa/(a + a + a) × a) + a).
2925 := ((aaa + aa + aa) × (aa + aa)/a − a)/a.
2926 := (aaa + aa + aa) × (aa + aa)/(a × a).
2927 := ((aaa + aa + aa) × (aa + aa)/a + a)/a.
2928 := (aa + aa + a + a) × (aaa + aa)/(a × a).
2929 := ((aa + aa + a + a) × (aaa + aa)/a + a)/a.
2930 := ((aa + aa + a + a) × (aaa + aa)/a + a + a)/a.
2931 := ((aa + aa + a + a) × (aaa + aa)/a + a + a + a)/a.
2932 := ((aa + aa + a + a) × (aaa + aa)/a + a + a + a + a)/a.
2933 := ((aaaa − aaa − aa − aa) × (a + a + a)/a − a)/a.
2934 := (aaaa − aaa − aa − aa) × (a + a + a)/(a × a).
2934 := ((aaaa − aaa − aa − aa) × (a + a + a)/a + a)/a.
2936 := (aaaa − aa + a) × (aa − a − a − a)/((a + a + a) × a).
2937 := (aaa − aa − aa) × (aaa − aa − a)/((a + a + a) × a).
2938 := (aaa−aa−aa−aa)×(aaa+a+a)/((a+a+a)×a).
2939 := ((aaa + aaa + aa + aa + a) × (aa + a)/a − a)/a.
2940 := (aaa + aaa + aa + aa + a) × (aa + a)/(a × a).
2941 := ((aaaa + a + a)/(aa + aa − a) × aaa − a)/(a + a).
2942 := ((aaaa + a + a)/(aa + aa − a) × aaa + a)/(a + a).
2943 := (a−aaa+a+a)×(a−aaa+a)/((a+a+a+a)×a).
2944 := ((aaaa + aaa) × (a + a + a)/(a + a) + aaaa)/a.
2945 := ((aaa + aa + aa + a) × (aa + aa)/a − a − a − a)/a.
2946 := ((aaa + aa + aa + a) × (aa + aa)/a − a − a)/a.
2947 := ((aaa + aa + aa + a) × (aa + aa)/a − a)/a.
2948 := (aaa + aa + aa + a) × (aa + aa)/(a × a).
2949 := ((aaa + aa + aa + a) × (aa + aa)/a + a)/a.
2950 := ((aa + aa + a + a) × (aaa + aa + a)/a − a − a)/a.
2951 := ((aa + aa + a + a) × (aaa + aa + a)/a − a)/a.
2952 := (aa + aa + a + a) × (aaa + aa + a)/(a × a).
2953 := ((aa + aa + a + a) × (aaa + aa + a)/a + a)/a.
25
2954 := (aaa + aaa − aa) × (aa + a + a + a)/(a × a).
2955 := ((aaa + aaa − aa) × (aa + a + a + a)/a + a)/a.
2956 := ((aaa + aaa − aa) × (aa + a + a + a)/a + a + a)/a.
2957 := ((aaa+aaa−aa)×(aa+a+a+a)/a+a+a+a)/a.
2958 := ((aaaa − aaa − aa) × (a + a + a)/a − aa + a + a)/a.
2959 := ((aaaa − aa − aa − aa)/(a + a) × aa − aa)/(a + a).
2960 := (aaaa − a) × (aa − a − a − a)/((a + a + a) × a).
2961 := ((aaaaa − aa)/(aa + a) × (a + a) + aaaa)/a.
2962 := ((aaaaa + a)/(aa + a) × (a + a) + aaaa − a)/a.
2963 := ((aaaaa + a)/(aa + a) × (a + a) + aaaa)/a.
2964 := (aaaa − aaa − aa − a) × (a + a + a)/(a × a).
2965 := ((aaaa − aa − aa − aa)/(a + a) × aa + a)/(a + a).
2966 := ((aaaa − aaa − aa) × (a + a + a)/a − a)/a.
2967 := (aaaa − aaa − aa) × (a + a + a)/(a × a).
2968 := (aaaa + a + a) × (aa − a − a − a)/((a + a + a) × a).
2969 := ((aaaa − aa) × aa/(a + a) − aaa − a)/(a + a).
2970 := (a − aaa + a + a) × (a − aaa)/((a + a + a + a) × a).
2971 := ((aaaa−aa)×aa/(a+a)−aaa+a+a+a)/(a+a).
2972 := (aaaa × aa − aaa × (a + a + a))/(a + a)/(a + a).
2973 := (aaaa − aaa − aa + a + a) × (a + a + a)/(a × a).
2974 := (aaa/(a + a + a) × aaa − aaaa − aa − aa)/a.
2975 := ((aaaa − aa) × aa/(a + a) − aaa + aa)/(a + a).
2976 := ((aaaa − aaa − a) × (a + a + a)/a − aa − aa + a)/a.
2977 := ((aaaaa − aaa) × (a + a + a)/aa − aa − aa − a)/a.
2978 := ((aaaaa − aaa) × (a + a + a)/aa − aa − aa)/a.
2979 := (aaaaaa × (a + a + a)/aaa − aa − aa − a − a)/a.
2980 := (aaaaaa × (a + a + a)/aaa − aa − aa − a)/a.
2981 := (aaaaaa × (a + a + a)/aaa − aa − aa)/a.
2982 := (aaaaaa × (a + a + a)/aaa − aa − aa + a)/a.
2983 := (aaaaaa × (a + a + a)/aaa − aa − aa + a + a)/a.
2984 := (aaa/(a + a + a) × aaa − aaaa − aa − a)/a.
2985 := (aaa/(a + a + a) × aaa − aaaa − aa)/a.
2986 := (aaa/(a + a + a) × aaa − aaaa − aa + a)/a.
2987 := ((aaaa − aaa − a) × (a + a + a)/a − aa + a)/a.
2988 := (aaa + aaa + aaa − a) × (aa − a − a)/(a × a).
2989 := ((aaaaa − aaa) × (a + a + a)/aa − aa)/a.
2990 := (aaaaaa × (a + a + a)/aaa − aa − a − a)/a.
2991 := (aaaaaa × (a + a + a)/aaa − aa − a)/a.
2992 := (aaaaaa × (a + a + a)/aaa − aa)/a.
2993 := (aaaaaa × (a + a + a)/aaa − aa + a)/a.
2994 := (aaaa − aaa − a − a) × (a + a + a)/(a × a).
2995 := (aaa/(a + a + a) × aaa − aaaa − a)/a.
2996 := (aaa/(a + a + a) × aaa − aaaa)/a.
2997 := (aaaa − aaa − a) × (a + a + a)/(a × a).
2998 := ((aaaa − aaa − a) × (a + a + a)/a + a)/a.
2999 := ((aaaaa − aaa) × (a + a + a)/aa − a)/a.
3000 := (aaaa − aaa) × (a + a + a)/(a × a).
3001 := (aaaaaa × (a + a + a)/aaa − a − a)/a.
3002 := (aaaaaa × (a + a + a)/aaa − a)/a.
3003 := aaaaaa × (a + a + a)/aaa/a.
3004 := (aaaaaa × (a + a + a)/aaa + a)/a.
3005 := (aaaaaa × (a + a + a)/aaa + a + a)/a.
3006 := (aaaa − aaa + a + a) × (a + a + a)/(a × a).
3007 := (aaa/(a + a + a) × aaa − aaaa + aa)/a.
3008 := ((aaaa + a) × aa/(a + a) − aaa + aa)/(a + a).
3009 := (aaaa − aaa + a + a + a) × (a + a + a)/(a × a).
3010 := ((aaaaa − aaa) × (a + a + a)/aa + aa − a)/a.
3011 := ((aaaaa − aaa) × (a + a + a)/aa + aa)/a.
3012 := ((aaaaa − aaa) × (a + a + a)/aa + aa + a)/a.
3013 := (aaaaaa × (a + a + a)/aaa + aa − a)/a.
3014 := (aaaaaa × (a + a + a)/aaa + aa)/a.
3015 := (aaaaaa × (a + a + a)/aaa + aa + a)/a.
3016 := (aaaaaa × (a + a + a)/aaa + aa + a + a)/a.
3017 := (aaa × aaa − (aa + aa + a) × aa)/(a + a)/(a + a).
26
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3018 := ((aaaaa − a) × (a + a + a) − (aa + a) × aa)/(aa × a).
3019 := ((aaaaa − a) × (a + a + a)/aa − aa)/a.
3020 := ((aaaaa − a) × (a + a + a)/aa − aa + a)/a.
3021 := ((aaaa − aa) × aa/(a + a) − aa + a + a + a)/(a + a).
3022 := ((aaaaa + aa − a) × (a + a + a) − aa × aa)/(aa × a).
3023 := ((aa + aa + aa) × (aaaa − aa)/(aa + a) − a − a)/a.
3024 := ((aaaa − aa) × aa/(a + a) − a − a)/(a + a).
3025 := (aaaa − aa) × aa/((a + a) × (a + a)).
3026 := ((aaaa − aa) × aa/(a + a) + a + a)/(a + a).
3027 := (aaaaa − aa − a) × (a + a + a)/(aa × a).
3028 := (aaaaa + aaaa − aaa + a)/(a + a + a + a).
3029 := (aaa + aaa + aa) × (aa + a + a)/(a × a).
3030 := (aaaaa − a) × (a + a + a)/(aa × a).
3031 := ((aaaaa − a) × (a + a + a)/aa + a)/a.
3032 := ((aaaa − aa) × aa/(a + a) + aa + a + a + a)/(a + a).
3033 := (aaaa − aaa + aa) × (a + a + a)/(a × a).
3034 := (aaa+aa+a)/(a+a+a)×(aaa+aaa)/(a+a+a).
3035 := (aaaaa−a)×(a+a+a)/(aa×a)+(aa−a)/(a+a).
3036 := ((aaaa − aa) × aa/(a + a) + aa + aa)/(a + a).
3037 := ((aaaaa−a)×(a+a+a)/aa+aa−a−a−a−a)/a.
3038 := ((aaaaa − aa − a) × (a + a + a) + aa × aa)/(aa × a).
3039 := ((aaa × aaa − aa × aa)/(a + a) − aa − aa)/(a + a).
3040 := ((aaaaa − a) × (a + a + a)/aa + aa − a)/a.
3041 := ((aaaaa − a) × (a + a + a)/aa + aa)/a.
3042 := (aaa + aaa + aa + a) × (aa + a + a)/(a × a).
3043 := ((aaaa − a) × aa/(a + a) + a)/(a + a) − (aaa − a)/aa.
3044 := ((aaa × aaa − aa × aa)/(a + a) − aa − a)/(a + a).
3045 := ((aaa × aaa − aa × aa)/(a + a) − aa + a)/(a + a).
3046 := ((aaaa − a) × aa/(a + a) − aa − a − a)/(a + a).
3047 := ((aaaa − a) × aa/(a + a) − aa)/(a + a).
3048 := ((aaaa − a) × aa/(a + a) − aa + a + a)/(a + a).
3049 := ((aaa × aaa − aa × aa)/(a + a) − a − a)/(a + a).
3050 := (aa + aa + a + a + a) × (aaa + aa)/(a × a).
3051 := ((aaaa − a) × aa/(a + a) − a − a − a)/(a + a).
3052 := ((aaaa − a) × aa/(a + a) − a)/(a + a).
3053 := ((aaaa − a) × aa/(a + a) + a)/(a + a).
3054 := ((aaaa − a) × aa/(a + a) + a + a + a)/(a + a).
3055 := (aaaa + aaa)/(a + a) × (aa − a)/(a + a).
3056 := ((aaaa + a)/(a + a + a + a) × aa − a − a)/a.
3057 := ((aaaa + a)/(a + a + a + a) × aa − a)/a.
3058 := (aaaa + a) × aa/(a + a)/(a + a).
3059 := ((aaaa + a) × aa/(a + a) + a + a)/(a + a).
3060 := (aaaaa + aaa − a − a) × (a + a + a)/(aa × a).
3061 := (aaaaa + aaaa + aa + aa)/(a + a + a + a).
3062 := ((aaaa + a) × aa/(a + a) + aa − a − a − a)/(a + a).
3063 := ((aaaa + a) × aa/(a + a) + aa − a)/(a + a).
3064 := ((aaaa + a) × aa/(a + a) + aa + a)/(a + a).
3065 := ((aaaa+a)/(a+a+a+a)×aa+aa−a−a−a−a)/a.
3066 := (aaaa − aaa + aa + aa) × (a + a + a)/(a × a).
3067 := ((aaaaa − a) × (aa − a − a)/aa + aaa)/(a + a + a).
3068 := ((aaaa + a) × aa/(a + a) + aa + aa − a − a)/(a + a).
3069 := ((aaaa + a) × aa/(a + a) + aa + aa)/(a + a).
3070 := ((aaaa + a) × aa/(a + a) + aa + aa + a + a)/(a + a).
3071 := (aaa + aaa + aaa − a) × aaa/((aa + a) × a).
3072 := (aaa × aaa − (a + a + a) × aa)/((a + a + a + a) × a).
3073 := ((aaa + aaa + aaa − a) × aaa/(aa + a) + a + a)/a.
3074 := ((aaaa + aa) × aa/(a + a) − aa − aa − a)/(a + a).
3075 := (aa + aa + a + a + a) × (aaa + aa + a)/(a × a).
3076 := ((aaa−aa)/(a+a)×(aaa+aa+a)+a+a)/(a+a).
3077 := (aaa + a)/(a + a) × (aaa − a)/(a + a) − (a + a + a)/a.
3078 := ((aaa + aa) × aaaa/aa − aa + a)/(a + a + a + a).
3079 := ((aaa + a)/(a + a) × (aaa − a) − a − a)/(a + a).
3080 := (aaa + a)/(a + a) × (aaa − a)/(a + a).
3081 := ((aaa + a)/(a + a) × (aaa − a) + a + a)/(a + a).
3082 := (aaa + aa + aa + a) × (aa + aa + a)/(a × a).
3083 := (aaaaa + aaaa + aaa − a)/(a + a + a + a).
3084 := ((aaaa + aa) × aa/(a + a) − a − a − a)/(a + a).
3085 := ((aaaa + aa) × aa/(a + a) − a)/(a + a).
3086 := ((aaaa + aa) × aa/(a + a) + a)/(a + a).
3087 := ((aaaa + aa) × aa/(a + a) + a + a + a)/(a + a).
3088 := ((aaaa − a) × (a + a + a) − (aa + aa) × aa)/(a × a).
3089 := ((aaaa−a)×aa/(a+a)−a)/(a+a)+aaa/(a+a+a).
3090 := ((aaaa + aa) × aa/(a + a) + aa − a − a)/(a + a).
3091 := ((aaaa + aa) × aa/(a + a) + aa)/(a + a).
3092 := ((aaaa + aa) × aa/(a + a) + aa + a + a)/(a + a).
3093 := (aaaaa + a)/(a + a + a) − (aaaa + aaa)/(a + a).
3094 := (aaa + aaa − a) × (aa + a + a + a)/(a × a).
3095 := (aaa + a) × aaa/((a + a) × (a + a)) − (aa + a + a)/a.
3096 := (aaa + aaa + aaa + aa) × (aa − a − a)/(a × a).
3097 := ((aaa + a) × aaa/(a + a) − aa − aa)/(a + a).
3098 := ((aaa + a) × aaa/(a + a) − aa − aa + a + a)/(a + a).
3099 := ((aa + aa + aa − a − a) × (aaa − aa)/a − a)/a.
3100 := (aa + aa + aa − a − a) × (aaa − aa)/(a × a).
3101 := ((aaa + a) × aaa/(a + a) − aa − a − a − a)/(a + a).
3102 := ((aaa + a) × aaa/(a + a) − aa − a)/(a + a).
3103 := ((aaa + a) × aaa/(a + a) − aa + a)/(a + a).
3104 := ((aaa + a) × aaa/(a + a) − aa + a + a + a)/(a + a).
3105 := ((aaa × aaa + aa × aa)/(a + a) − aa)/(a + a).
3106 := ((aaa + aa + a) × aaaa/aa + a)/(a + a + a + a).
3107 := ((aaa + a) × aaa/(a + a) − a − a)/(a + a).
3108 := (aaa + a) × aaa/((a + a) × (a + a)).
3109 := ((aaa + a) × aaa/(a + a) + a + a)/(a + a).
3110 := ((aaa × aaa + aa × aa)/(a + a) − a)/(a + a).
3111 := (aaaa × (a + a + a) − aaa × (a + a))/(a × a).
3112 := (aaaaaa/aaa × (a + a) + aaaa − a)/a.
3113 := ((aaaa + a) × aa/(a + a) + aaa − a)/(a + a).
3114 := ((aaa + a) × aaa/(a + a) + aa + a)/(a + a).
3115 := ((aaa + a) × aaa/(a + a) + aa + a + a + a)/(a + a).
3116 := ((aaaa+a)×(a+a+a)−(aaa−a)×(a+a))/(a×a).
3117 := ((aaa×aaa+aa×aa)/(a+a)+aa+a+a)/(a+a).
3118 := ((aaaa + aa + aa + a)/(a + a) × aa − a)/(a + a).
3119 := ((aaa + a) × aaa/(a + a) + aa + aa)/(a + a).
3120 := ((aaaaa − a)/aa × (a + a) + aaaa − aa)/a.
3121 := ((aaaa − aaa) × (a + a + a) + aa × aa)/(a × a).
3122 := (aaa + aaa + a) × (aa + a + a + a)/(a × a).
3123 := ((aaaaa−a)/aa×(a+a)+aaaa−aa+a+a+a)/a.
3124 := ((aaaa + aa + aa + a)/(a + a) × aa + aa)/(a + a).
3125 := ((aaa + a) × (aaa + a)/(a + a) − aa − aa)/(a + a).
3126 := ((aaaaa−aa−a)/aa×(a+a)+aaaa−a−a−a)/a.
3127 := ((aaaaa − aa − a)/aa × (a + a) + aaaa − a − a)/a.
3128 := ((aaaaa − aa − a)/aa × (a + a) + aaaa − a)/a.
3129 := ((aaaaa − aa − a)/aa × (a + a) + aaaa)/a.
3130 := ((aaa + a) × (aaa + a)/(a + a) − aa − a)/(a + a).
3131 := ((aaaaa − a)/aa × (a + a) + aaaa)/a.
3132 := ((aaaaa − a)/aa × (a + a) + aaaa + a)/a.
3133 := ((aaaaa − a)/aa × (a + a) + aaaa + a + a)/a.
3134 := ((aaaaa + a)/(a + a + a) × aa − a − a)/(aa + a + a).
3135 := (aaa + a + a + a) × (aaa − a)/((a + a + a + a) × a).
3136 := (aaa + a) × (aaa + a)/((a + a) × (a + a)).
3137 := ((aaa + a) × (aaa + a)/(a + a) + a + a)/(a + a).
3138 := ((aaaaa−aa−a)/aa×(a+a)+aaaa+aa−a−a)/a.
3139 := (aaaaa − aa)/(a + a + a) − (aaaa + aa)/(a + a).
3140 := (aaaa × (a + a + a)/aa + aa) × (aa − a)/(a × a).
3141 := ((aaaaa − a) × (a + a + a)/aa + aaa)/a.
3142 := ((aaa + a) × (aaa + a)/(a + a) + aa + a)/(a + a).
3143 := ((aaa+a)×(aaa+a)/(a+a)+aa+a+a+a)/(a+a).
3144 := ((aaaaa − a)/aa × (a + a) + aaaa + aa + a + a)/a.
3145 := (aa + aa + aa + a) × (aaaa − a)/((aa + a) × a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3146 := (aaaa + aa + aa + aa) × aa/((a + a) × (a + a)).
3147 := ((aaaa + aa) × aa/(a + a) + aaa + aa + a)/(a + a).
3148 := (aaaaa + a)/(a + a + a) − (aaaa + a)/(a + a).
3149 := (aaaaa + a)/(a + a + a) − (aaaa − a)/(a + a).
3150 := (aaaaa − aa)/(a + a + a) − (aaaa − aa)/(a + a).
3151 := (aaaaa + aa − a)/(a + a + a) − (aaaa + a)/(a + a).
3152 := ((aaaaa − a) × (a + a + a)/aa + aaa + aa)/a.
3153 := ((aaaa − a) × aa/(a + a) − a)/(a + a) + aaaa/aa.
3154 := (aaaaa + a)/(a + a + a) − (aaaa − aa)/(a + a).
3155 := (aaaaa + a)/(a + a + a) − (aaaa − aa)/(a + a) + a/a.
3156 := (aaa+aa+aa+aa)×(aa+aa)/(a×a)−(aa+a)/a.
3157 := (aaa + aa + aa + aa) × (aa + aa)/(a × a) − aa/a.
3158 := ((aaa + a) × aaa/(a + a) + aaa − aa)/(a + a).
3159 := ((aaaa−a)×aaa/(a+a+a)−a−a−a)/(aa+a+a).
3160 := ((aaaa−a)×aaa/(a+a+a)+aa−a)/(aa+a+a).
3161 := ((aa + aa + aa − a − a) × (aaaa + aa)/aa − a)/a.
3162 := (aaaa × aaa/(a + a + a) − a)/(aa + a + a).
3163 := ((aaa + a) × aaa/(a + a) + aaa − a)/(a + a).
3164 := (aaa + a + a) × (aaa + a)/((a + a + a + a) × a).
3165 := (aaa + aaa − aa) × (aa + a + a + a + a)/(a × a).
3166 := ((aaa + a + a) × aaa + aa × aa)/((a + a) × (a + a)).
3167 := ((aaa + aa + aa + aa) × (aa + aa)/a − a)/a.
3168 := (aaa + aa + aa + aa) × (aa + aa)/(a × a).
3169 := ((aaa + a) × aaa/(a + a) + aaa + aa)/(a + a).
3170 := ((aaa+a)×aaa/(a+a)+aaa+aa+a+a)/(a+a).
3171 := ((aaa + aaa + aa + aa) × (aa + a + a)/a − a)/a.
3172 := (aaa + aaa + aa + aa) × (aa + a + a)/(a × a).
3173 := ((aaa + aaa + aa + aa) × (aa + a + a)/a + a)/a.
3174 := (aaaaa − a − a)/(aa + aa − a) × (aa + a)/(a + a).
3175 := ((aaa+aaa+aa+aa)×(aa+a+a)/a+a+a+a)/a.
3176 := (((aaaa−aa)×(a+a+a)−aa×aa)/a−a−a−a)/a.
3177 := (((aaaa − aa) × (a + a + a) − aa × aa)/a − a − a)/a.
3178 := (aaaaa+aa+a)×(aa+a)/((aa+aa−a)×(a+a)).
3179 := ((aaaa − aa) × (a + a + a) − aa × aa)/(a × a).
3180 := (((aaaa − aa) × (a + a + a) − aa × aa)/a + a)/a.
3181 := (aaa + a)/(a + a) × (aaa − a)/(a + a) + aaaa/aa.
3182 := (aaa − aa − aa − a − a − a) × aaa/((a + a + a) × a).
3183 := ((aaa + aaa) × (aaa + a)/(aa + a) + aaaa)/a.
3184 := ((aaa + aaa + aa + aa) × (aa + a + a)/a + aa + a)/a.
3185 := (aaa + aaa + aa + aa + a) × (aa + a + a)/(a × a).
3186 := ((aaa + a) × (aaa + a)/(a + a) + aaa − aa)/(a + a).
3187 := ((aa + aa + aa − a) × (aaa − aa)/a − aa − a − a)/a.
3188 := ((aa + aa + aa − a) × (aaa − aa)/a − aa − a)/a.
3189 := ((aa + aa + aa − a) × (aaa − aa)/a − aa)/a.
3190 := ((aa + aa + aa − a) × (aaa − aa)/a − aa + a)/a.
3191 := ((aaa + a) × (aaa + a)/(a + a) + aaa − a)/(a + a).
3192 := (aaa + a + a + a) × (aaa + a)/((a + a + a + a) × a).
3193 := ((aaa−aa−aa)×(aaa−a−a−a)/(a+a+a)−aa)/a.
3194 := (((aaaa−a−a)×(a+a+a)−aa×aa)/a−aa−a)/a.
3195 := (((aaaa − a − a) × (a + a + a) − aa × aa)/a − aa)/a.
3196 := (((aaaa−a−a)×(a+a+a)−aa×aa)/a−aa+a)/a.
3197 := (aaaa+a)×(aa+aa+a)/((a+a)×(a+a+a+a)).
3198 := ((aa + aa + aa − a) × (aaa − aa)/a − a − a)/a.
3199 := ((aa + aa + aa − a) × (aaa − aa)/a − a)/a.
3200 := (aa + aa + aa − a) × (aaa − aa)/(a × a).
3201 := (aaaa × (a + a + a) − (aa + a) × aa)/(a × a).
3202 := ((aa + aa + aa − a) × (aaa − aa)/a + a + a)/a.
3203 := ((aa + aa + aa − a) × (aaa − aa)/a + a + a + a)/a.
3204 := (aaa−aa−aa)×(aaa−a−a−a)/((a+a+a)×a).
3205 := (((aaaa − a − a) × (a + a + a) − aa × aa)/a − a)/a.
3206 := ((aaaa − a − a) × (a + a + a) − aa × aa)/(a × a).
3207 := (((aaaa − a) × (a + a + a) − aa × aa)/a − a − a)/a.
3208 := (((aaaa − a) × (a + a + a) − aa × aa)/a − a)/a.
3209 := ((aaaa − a) × (a + a + a) − aa × aa)/(a × a).
27
3210 := ((aa + aa + aa − a) × (aaa − aa)/a + aa − a)/a.
3211 := (aaaa + aaaa + aaaa − aaa − aa)/a.
3212 := (aaaa × (a + a + a) − aa × aa)/(a × a).
3213 := ((aaaa × (a + a + a) − aa × aa)/a + a)/a.
3214 := ((aaaa × (a + a + a) − aa × aa)/a + a + a)/a.
3215 := ((aaaa + a) × (a + a + a) − aa × aa)/(a × a).
3216 := (aaa + aa + aa + a) × (aa + aa + a + a)/(a × a).
3217 := ((aaa + aa + aa + a) × (aa + aa + a + a)/a + a)/a.
3218 := ((aaa+aa+aa+a)×(aa+aa+a+a)/a+a+a)/a.
3219 := (aaa − aa − aa − a − a) × aaa/((a + a + a) × a).
3220 := (aaa+a+a+a+a)×(aaa+a)/((a+a+a+a)×a).
3221 := ((aa − a − a) × aaa + aaaa × (a + a))/(a × a).
3222 := (aaaa + aaaa + aaaa − aaa)/a.
3223 := (aaaa + aaaa + aaaa − aaa + a)/a.
3224 := (aaaa + aaaa + aaaa − aaa + a + a)/a.
3225 := (aaaa + aaaa + aaaa − aaa + a + a + a)/a.
3226 := (aaaa + aaaa + aaaa − aaa + a + a + a + a)/a.
3227 := ((aa+aa+aa−a)×aaaa/aa−a−a−a−a−a)/a.
3228 := ((aa + aa + aa − a) × aaaa/aa − a − a − a − a)/a.
3229 := ((aa + aa + aa − a) × aaaa/aa − a − a − a)/a.
3230 := ((aa + aa + aa − a) × aaaa/aa − a − a)/a.
3231 := ((aa + aa + aa − a) × aaaa/aa − a)/a.
3232 := (aa + aa + aa − a) × aaaa/(aa × a).
3233 := ((aa + aa + aa − a) × aaaa/aa + a)/a.
3234 := ((aa + aa + aa − a) × aaaa/aa + a + a)/a.
3235 := ((aa + aa + aa − a) × aaaa/aa + a + a + a)/a.
3236 := ((aa + aa + aa − a) × aaaa/aa + a + a + a + a)/a.
3237 := (aaaa−aa−aa−aa+a)×(aa+a)/((a+a)×(a+a)).
3238 := (aaaa − aaa) × (aa + a + a)/((a + a) × (a + a)) −
(aa + a)/a.
3239 := (aaaa−aaa)×(aa+a+a)/((a+a)×(a+a))−aa/a.
3240 := ((aa + aa + aa − a) × aaaa/aa + aa − a − a − a)/a.
3241 := ((aaaa−aa−a)×(aa+a)/(a+a)−aaa−a)/(a+a).
3242 := ((aaaa + aa − a) × (a + a + a) − aa × aa)/(a × a).
3243 := ((aa + aa + aa − a) × aaaa/aa + aa)/a.
3244 := ((aaaa − aa) × (aa + a)/(a + a) − aaa − a)/(a + a).
3245 := ((aaaa + aa) × (a + a + a) − aa × aa)/(a × a).
3246 := (((aaaa + aa) × (a + a + a) − aa × aa)/a + a)/a.
3247 := ((aaa + a) × (aaa + a)/(a + a) + aaa + aaa)/(a + a).
3248 := ((aaaa + aa + a) × (a + a + a) − aa × aa)/(a × a).
3249 := ((aaaa−aaa)×(aa+a+a)/(a+a)−a−a)/(a+a).
3250 := (aaaa − aaa) × (aa + a + a)/((a + a) × (a + a)).
3251 := ((aaaa−aaa)×(aa+a+a)/(a+a)+a+a)/(a+a).
3252 := ((aaaa + aa) × (aa + aa − a)/aa + aaaa − a)/a.
3253 := ((aaaa + aa) × (aa + aa − a)/aa + aaaa)/a.
3254 := ((aaa − aa − aa − a) × aaa/(a + a + a) − a − a)/a.
3255 := ((aaa − aa − aa − a) × aaa/(a + a + a) − a)/a.
3256 := (aaa − aa − aa − a) × aaa/((a + a + a) × a).
3257 := ((aaa − aa − aa − a) × aaa/(a + a + a) + a)/a.
3258 := ((aaa − aa − aa − a) × aaa/(a + a + a) + a + a)/a.
3259 := ((aaaa − aa − aa − a − a) × (a + a + a)/a − a − a)/a.
3260 := ((aaaa − aa − aa − a − a) × (a + a + a)/a − a)/a.
3261 := (aaaa − aa − aa − a − a) × (a + a + a)/(a × a).
3262 := (aaa + aaa + aa) × (aa + a + a + a)/(a × a).
3263 := ((aa + aa + aa − a) × (aaaa + aa)/aa − a)/a.
3264 := (aaaa − aa − aa − a) × (a + a + a)/(a × a).
3264 := ((aaaa − aa − aa − a) × (a + a + a)/a + a)/a.
3266 := ((aaaa − aa − aa) × (a + a + a)/a − a)/a.
3267 := (aaaa − aa − aa) × (a + a + a)/(a × a).
3268 := (aaaaaa + a)/(aa + aa + aa + a).
3269 := (aaaaaa + a)/(aa + aa + aa + a) + a/a.
3270 := (aaaa − aa − aa + a) × (a + a + a)/(a × a).
3271 := ((aaaa − aa − aa + a) × (a + a + a)/a + a)/a.
3272 := ((aaaa − aa − aa + a) × (a + a + a)/a + a + a)/a.
28
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3273 := (aaaa − aa − aa + a + a) × (a + a + a)/(a × a).
3273 := ((aaaa − aa − aa + a + a) × (a + a + a)/a + a)/a.
3275 := ((aa + aa + aa − a) × (aaaa + aa)/aa + aa)/a.
3276 := aaaaaa × (a + a + a) × (aa + a)/(aaa × aa × a).
3277 := (aaaa × (aa + a)/(a + a) − aaa − a)/(a + a).
3278 := (aaaa × (aa + a)/(a + a) − aaa + a)/(a + a).
3279 := (aaaa × (aa + a)/(a + a) − aaa + a + a + a)/(a + a).
3280 := ((aaaa + a) × (aa + a)/(a + a) − aaa − a)/(a + a).
3281 := ((aaaa + a) × (aa + a)/(a + a) − aaa + a)/(a + a).
3282 := ((aaa − aa − aa) × aaa/(a + a + a) − aa)/a.
3283 := (aaaa × (aa + a)/(a + a) − aaa + aa)/(a + a).
3284 := (aaaa×(aa+a)/(a+a)−aaa+aa+a+a)/(a+a).
3285 := ((aaaa + a)/(a + a) + aaaa/aa) × (aa − a)/(a + a).
3286 := ((aaaa + a) × (aa + a)/(a + a) − aaa + aa)/(a + a).
3287 := ((aa + aa + aa) × (aaaa − aa)/aa − aa − a − a)/a.
3288 := ((aaaaa − a) × (aa + a + a)/(aa + aa) + aa)/(a + a).
3289 := ((aa + aa + aa) × (aaaa − aa)/aa − aa)/a.
3290 := ((aa + aa + aa) × (aaaa − aa)/aa − aa + a)/a.
3291 := (aaaa − aa − a − a − a) × (a + a + a)/(a × a).
3292 := ((aaa − aa − aa) × aaa/(a + a + a) − a)/a.
3293 := (aaa − aa − aa) × aaa/((a + a + a) × a).
3294 := (aaaa − aa − a − a) × (a + a + a)/(a × a).
3295 := ((aaaa − aa − a − a) × (a + a + a)/a + a)/a.
3296 := ((aaaa − aa − a) × (a + a + a)/a − a)/a.
3297 := (aaaa − aa − a) × (a + a + a)/(a × a).
3298 := ((aaaa − aa − a) × (a + a + a)/a + a)/a.
3299 := ((aaaa − aa) × (a + a + a)/a − a)/a.
3300 := (aaaa − aa) × (a + a + a)/(a × a).
3301 := ((aaaa − aa) × (a + a + a)/a + a)/a.
3302 := ((aaaa − aa) × (a + a + a)/a + a + a)/a.
3303 := (aaaa − aa + a) × (a + a + a)/(a × a).
3304 := ((aaaa − aa + a) × (a + a + a)/a + a)/a.
3305 := ((aaaa − aa + a) × (a + a + a)/a + a + a)/a.
3306 := (aaaa − aa + a + a) × (a + a + a)/(a × a).
3307 := ((aaaa − aa + a + a) × (a + a + a)/a + a)/a.
3308 := ((aaaa − aa + a + a) × (a + a + a)/a + a + a)/a.
3309 := (aaaa−aa+a+a+a)×(aa+a)/((a+a)×(a+a)).
3310 := (aaaa + aaaa + aaaa − aa − aa − a)/a.
3311 := (aaaa + aaaa + aaaa − aa − aa)/a.
3312 := (aaaa + aaaa + aaaa − aa − aa + a)/a.
3313 := ((aaaa+aa+a)×(aa+a)/(a+a)−aaa−a)/(a+a).
3314 := ((aaaa+aa+a)×(aa+a)/(a+a)−aaa+a)/(a+a).
3315 := ((aa + aa + aa) × (aaaa − a − a)/aa − aa − a)/a.
3316 := ((aa + aa + aa) × (aaaa − a − a)/aa − aa)/a.
3317 := ((aa + aa + aa) × (aaaa − a − a)/aa − aa + a)/a.
3318 := ((aaaa − aa + a + a) × (a + a + a)/a + aa + a)/a.
3319 := (aaaa + aaaa + aaaa − aa − a − a − a)/a.
3320 := (aaaa + aaaa + aaaa − aa − a − a)/a.
3321 := (aaaa + aaaa + aaaa − aa − a)/a.
3322 := (aaaa + aaaa + aaaa − aa)/a.
3323 := (aaaa + aaaa + aaaa − aa + a)/a.
3324 := (aaaa − a − a − a) × (a + a + a)/(a × a).
3325 := ((aa + aa + aa) × (aaaa + a)/aa − aa)/a.
3326 := (aaaaa − aaaa − aa − aa)/(a + a + a).
3327 := (aaaa − a − a) × (a + a + a)/(a × a).
3328 := (aaaa × (aa + a)/(a + a) − aa + a)/(a + a).
3329 := (aaaaa − aaaa − aa − a − a)/(a + a + a).
3330 := (aaaa − a) × (a + a + a)/(a × a).
3331 := (aaaa + aaaa + aaaa − a − a)/a.
3332 := (aaaa × (a + a + a)/a − a)/a.
3333 := aaaa × (a + a + a)/(a × a).
3334 := (aaaa × (a + a + a)/a + a)/a.
3335 := (aaaa × (a + a + a)/a + a + a)/a.
3336 := (aaaa + a) × (a + a + a)/(a × a).
3337 := ((aaaa + a) × (a + a + a)/a + a)/a.
3338 := ((aaaa + a) × (a + a + a)/a + a + a)/a.
3339 := (aaaa + a + a) × (a + a + a)/(a × a).
3340 := (aaa + aaa + aaa + a) × (aa − a)/(a × a).
3341 := ((aaaa − a) × (a + a + a)/a + aa)/a.
3342 := (aaaa + a + a + a) × (a + a + a)/(a × a).
3343 := (aaaa × (a + a + a)/a + aa − a)/a.
3344 := (aaaa × (a + a + a)/a + aa)/a.
3345 := (aaaa × (a + a + a)/a + aa + a)/a.
3346 := (aaaa + aaaa + aaaa + aa + a + a)/a.
3347 := ((aa + aa + aa) × (aaaa + a)/aa + aa)/a.
3348 := ((aa + aa + aa) × (aaaa + a)/aa + aa + a)/a.
3349 := ((aa + aa + aa) × (aaaa + a)/aa + aa + a + a)/a.
3350 := (aaa + aaa + aaa + a + a) × (aa − a)/(a × a).
3351 := ((aaaa + aa − a) × (a + a + a)/a − aa − a)/a.
3352 := ((aaaa + aa − a) × (a + a + a)/a − aa)/a.
3353 := ((aaaa + aa − a) × (a + a + a)/a − aa + a)/a.
3354 := ((aaa + aa)/(a + a) × (aaa − a) − a − a)/(a + a).
3355 := (aaa + aa)/(a + a) × (aaa − a)/(a + a).
3356 := ((aaa + aa)/(a + a) × (aaa − a) + a + a)/(a + a).
3357 := (aaaa + aa − a − a − a) × (a + a + a)/(a × a).
3358 := ((aaaaa + a)/(aa + a) × aa − aaa − a)/(a + a + a).
3359 := ((aaaa + aaa)/(a + a) × aa − a − a − a)/(a + a).
3360 := (aaaa + aa − a − a) × (a + a + a)/(a × a).
3361 := ((aaaa + aaa)/(a + a) × aa + a)/(a + a).
3362 := ((aaaa + aaa)/(a + a) × aa + a + a + a)/(a + a).
3363 := (aaaa + aa − a) × (a + a + a)/(a × a).
3364 := ((aaaa + aa − a) × (a + a + a)/a + a)/a.
3365 := ((aaaa + aa − a) × (a + a + a)/a + a + a)/a.
3366 := (aaaa + aa) × (a + a + a)/(a × a).
3367 := aaaaaa/(a + a + a) × a/aa.
3368 := ((aaaa + aa + a) × (a + a + a)/a − a)/a.
3369 := (aaaa + aa + a) × (a + a + a)/(a × a).
3370 := ((aaaa + aa + a) × (a + a + a)/a + a)/a.
3371 := ((aaaa + aa + a) × (a + a + a)/a + a + a)/a.
3372 := (aaaa + aa + a + a) × (a + a + a)/(a × a).
3373 := ((aaaa + aa + a + a) × (a + a + a)/a + a)/a.
3374 := ((aaaa + aa + a + a) × (a + a + a)/a + a + a)/a.
3375 := (aaaa + aa + a + a + a) × (a + a + a)/(a × a).
3376 := ((aaaa + aa + a + a + a) × (a + a + a)/a + a)/a.
3377 := ((aaaa + aa + a + a + a) × (a + a + a)/a + a + a)/a.
3378 := aaaaaa/(a + a + a) × a/aa + aa/a.
3379 := ((aaa + aa) × aaa/(a + a) − aa − a − a)/(a + a).
3380 := ((aaa + aa) × aaa/(a + a) − aa)/(a + a).
3381 := ((aaa + aa) × aaa/(a + a) − aa + a + a)/(a + a).
3382 := ((aaa + aa + a) × (aaa − a)/(a + a) − a)/(a + a).
3383 := ((aaa + aa + a) × (aaa − a)/(a + a) + a)/(a + a).
3384 := ((aaa + aa) × aaa/(a + a) − a − a − a)/(a + a).
3385 := ((aaa + aa) × aaa/(a + a) − a)/(a + a).
3386 := ((aaa + aa) × aaa/(a + a) + a)/(a + a).
3387 := ((aaa + aa) × aaa/(a + a) + a + a + a)/(a + a).
3388 := ((aaaaa − aa)/(aa + a) × aa − aa)/(a + a + a).
3389 := (aaaa × (aa + a)/(a + a) + aaa + a)/(a + a).
3390 := ((aaa + aa) × aaa/(a + a) + aa − a − a)/(a + a).
3391 := ((aaa + aa) × aaa/(a + a) + aa)/(a + a).
3392 := ((aaa + aa) × aaa/(a + a) + aa + a + a)/(a + a).
3393 := (aaaa + aa + aa − a − a) × (a + a + a)/(a × a).
3394 := (aaaa × (aa + a)/(a + a) + aaa + aa)/(a + a).
3395 := ((aaaaa + a)/(aa + a) × aa − a)/(a + a + a).
3396 := (aaaa + aa + aa − a) × (a + a + a)/(a × a).
3397 := ((aaaa + aa + aa) × (a + a + a)/a − a − a)/a.
3398 := ((aaaa + aa + aa) × (a + a + a)/a − a)/a.
3399 := (aaaa + aa + aa) × (a + a + a)/(a × a).
3400 := (aa + aa + aa + a) × (aaa − aa)/(a × a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3401 := ((aa + aa + aa + a) × (aaa − aa)/a + a)/a.
3402 := (aaaa + aa + aa + a) × (a + a + a)/(a × a).
3403 := ((aaa + aa) × aaa/(a + a + a) − aaaa)/a.
3404 := aaaaaa/(aa + aa + aa) + aaa/(a + a + a).
3405 := (aaaa + aa + aa + a + a) × (a + a + a)/(a × a).
3406 := ((aaaa + aa + aa + a + a) × (a + a + a)/a + a)/a.
3407 := ((aaaa + aa + aa + a + a) × (a + a + a)/a + a + a)/a.
3407 := ((aaaa+aa+aa+a+a)×(a+a+a)/a+a+a+a)/a.
3409 := (((aaa − aa) × (aa + aa) + aaa × aa)/a − aa − a)/a.
3410 := ((aaa + aa) × (aaa + a)/(a + a) − aa − a)/(a + a).
3411 := ((aa + aa + aa + a) × (aaa − aa)/a + aa)/a.
3412 := ((aa + aa + aa + a) × (aaa − aa)/a + aa + a)/a.
3413 := ((aa + aa + aa + a) × (aaa − aa)/a + aa + a + a)/a.
3414 := ((aaa + aa) × aaa/(a + a + a) − aaaa + aa)/a.
3415 := ((aaa + aa) × (aaa + a)/(a + a) − a − a)/(a + a).
3416 := (aaa + aa) × (aaa + a)/((a + a) × (a + a)).
3417 := ((aaa + aa) × (aaa + a)/(a + a) + a + a)/(a + a).
3418 := ((aaaa − aa − a) × (a + a + a) + aa × aa)/(a × a).
3419 := ((aaaa − aa − a) × (a + a) + aaa × aa)/(a × a).
3420 := (((aaa − aa) × (aa + aa) + aaa × aa)/a − a)/a.
3421 := ((aaa − aa) × (aa + aa) + aaa × aa)/(a × a).
3422 := ((aa + aa + aa + a) × aaaa/aa − aa − a)/a.
3423 := ((aa + aa + aa + a) × aaaa/aa − aa)/a.
3424 := ((aa + aa + aa + a) × aaaa/aa − aa + a)/a.
3425 := ((aaaa + a) × aaa/(aa + a) − aa)/(a + a + a).
3426 := (aaaaa+a)/(a+a+a)−(aaaa+a)/(a+a+a+a).
3437 := ((aa + aa + aa) × (aaaa − a − a)/aa + aaa − aa)/a.
3428 := ((aaaa − a − a) × (a + a) + (aaa − a) × aa)/(a × a).
3429 := ((aaaa + a) × aaa/(aa + a) + a)/(a + a + a).
3430 := ((aaaa × (a + a) + (aaa − a) × aa)/a − a − a)/a.
3431 := ((aaaa × (a + a) + (aaa − a) × aa)/a − a)/a.
3432 := (aaaa × (a + a) + (aaa − a) × aa)/(a × a).
3433 := (aaaa + aaaa + aaaa + aaa − aa)/a.
3434 := (aa + aa + aa + a) × aaaa/(aa × a).
3435 := ((aa + aa + aa + a) × aaaa/aa + a)/a.
3436 := ((aa + aa + aa + a) × aaaa/aa + a + a)/a.
3437 := ((aa + aa + aa + a) × aaaa/aa + a + a + a)/a.
3438 := ((aa + aa + aa) × (aaaa − a − a)/aa + aaa)/a.
3439 := ((aaaa − a − a) × (a + a) + aaa × aa)/(a × a).
3440 := (aaa + aaa + aaa + aa) × (aa − a)/(a × a).
3441 := ((aaaa − a) × (a + a) + aaa × aa)/(a × a).
3442 := (aaaa + aaaa + aaaa + aaa − a − a)/a.
3443 := (aaaa × (a + a) + aaa × aa)/(a × a).
3444 := (aaa + aa + a) × (aaa + a)/((a + a) × (a + a)).
3445 := ((aaaa + a) × (a + a) + aaa × aa)/(a × a).
3446 := ((aaa + a + a) × (aaa + aa)/(a + a) − a)/(a + a).
3447 := ((aaa + a + a) × (aaa + aa)/(a + a) + a)/(a + a).
3448 := ((aaa + aaa + aaa + aa + a) × (aa − a)/a − a − a)/a.
3449 := ((aaa + aaa + aaa + aa + a) × (aa − a)/a − a)/a.
3450 := (aaa + aaa + aaa + aa + a) × (aa − a)/(a × a).
3451 := ((aaaa − a) × (a + a + a) + aa × aa)/(a × a).
3452 := ((aaaa × (a + a + a) + aa × aa)/a − a − a)/a.
3453 := ((aaaa × (a + a + a) + aa × aa)/a − a)/a.
3454 := (aaaa × (a + a + a) + aa × aa)/(a × a).
3455 := ((aaaa × (a + a + a) + aa × aa)/a + a)/a.
3456 := (((aaaa + a) × (a + a + a) + aa × aa)/a − a)/a.
3457 := ((aaaa + a) × (a + a + a) + aa × aa)/(a × a).
3458 := (((aaaa + a) × (a + a + a) + aa × aa)/a + a)/a.
3459 := (((aaaa + a) × (a + a + a) + aa × aa)/a + a + a)/a.
3460 := ((aaaa + a + a) × (a + a + a) + (aa × aa))/(a × a).
3461 := ((aaa + aaa + a + a) × (aa − a) + aaa × aa)/(a × a).
3462 := ((aaaa − a) × (a + a + a) + (aa + a) × aa)/(a × a).
3463 := ((aaaa+a+a)×(aaa+a)/(aa+a)+a)/(a+a+a).
3464 := ((aaaa × (a + a + a) + (aa + a) × aa)/a − a)/a.
29
3465 := (aaaa × (a + a + a) + (aa + a) × aa)/(a × a).
3466 := ((aaaa × (a + a + a) + (aa + a) × aa)/a + a)/a.
3467 := ((aaaa + aa + a) × (a + a) + aaa × aa)/(a × a).
3468 := (aaaa + aa)/aa × (aa + aa + aa + a)/a.
3469 := ((aaaa + aa)/aa × (aa + aa + aa + a) + a)/a.
3470 := ((aa + aa + aa − a − a) × (aaa + a)/a − a − a)/a.
3471 := ((aa + aa + aa − a − a) × (aaa + a)/a − a)/a.
3472 := (aa + aa + aa − a − a) × (aaa + a)/(a × a).
3473 := ((aa + aa + aa − a − a) × (aaa + a)/a + a)/a.
3474 := ((aa + aa + aa − a − a) × (aaa + a)/a + a + a)/a.
3475 := ((aa + aa + aa − a − a) × (aaa + a)/a + a + a + a)/a.
3476 := ((aaaa + aa) × (a + a) + (aaa + a) × aa)/(a × a).
3477 := (aaa + a + a + a) × (aaa + aa)/((a + a + a + a) × a).
3478 := (aaaa + aaa)/(aa + a + a) × aaa/(a + a + a).
3489 := (((aaaa+aa+a)×(a+a+a)+aa×aa)/a−aa)/a.
3480 := (aaaaa − (aaa + aa) × aa/(a + a))/(a + a + a).
3481 := (aaaaa−aaa×(aa+a)/(a+a)−a−a)/(a+a+a).
3482 := ((aa + aa + aa − a − a) × (aaa + a)/a + aa − a)/a.
3483 := ((aa + aa + aa − a − a) × (aaa + a)/a + aa)/a.
3484 := (aaaaa − (aaa + a) × aaa/(a + a + a) + a)/(a + a).
3485 := ((aaaa + aa + aa − a) × (a + a) + aaa × aa)/(a × a).
3486 := (((aaaa + aa) × (a + a + a) + aa × aa)/a − a)/a.
3487 := ((aaaa + aa) × (a + a + a) + aa × aa)/(a × a).
3488 := (aa + aa + aa − a) × (aaa − a − a)/(a × a).
3489 := (((aaaa + aa + a) × (a + a + a) + aa × aa)/a − a)/a.
3490 := ((aaaa + aa + a) × (a + a + a) + aa × aa)/(a × a).
3491 := ((aaaa + aa) × (aaa + a)/(aa + a) + a)/(a + a + a).
3492 := (((aaaa+aa+a+a)×(a+a+a)+aa×aa)/a−a)/a.
3493 := ((aaaa+aa+a+a)×(a+a+a)+aa×aa)/(a×a).
3494 := (((aaaa+aa+a+a)×(a+a+a)+aa×aa)/a+a)/a.
3495 := (aaa + aaa + aa) × (aa + a + a + a + a)/(a × a).
3496 := ((aaa + aaa + aa) × (aa + a + a + a + a)/a + a)/a.
3497 := ((aaa+aaa+aa)×(aa+a+a+a+a)/a+a+a)/a.
3498 := (aaaaa − (aaa + a)/(a + a) × aa − a)/(a + a + a).
3499 := ((aa + aa + aa + a + a) × (aaa − aa)/a − a)/a.
3500 := (aa + aa + aa + a + a) × (aaa − aa)/(a × a).
3501 := (aaaaa − aaa/(a + a + a) × aaa − a − a)/(a + a).
3502 := (aaaaa − aaa/(a + a + a) × aaa)/(a + a).
3503 := (aa + aa + aa − a − a) × (aaa + a + a)/(a × a).
3504 := (aaaa × (a + a + a)/aa − aa) × (aa + a)/(a × a).
3505 := ((aaaa × (a + a + a)/aa − aa) × (aa + a)/a + a)/a.
3506 := ((aaaa + aa + aa − a) × (a + a + a)/a + aaa − a)/a.
3507 := ((aaaa + aa + aa − a) × (a + a + a)/a + aaa)/a.
3508 := ((aa + aa + aa − a) × (aaa − a)/a − a − aa)/a.
3509 := ((aa + aa + aa − a) × (aaa − a)/a − aa)/a.
3510 := ((aa + aa + aa − a) × (aaa − a)/a − aa + a)/a.
3511 := ((aa + aa + aa − a) × (aaa − a)/a − aa + a + a)/a.
3512 := ((aa + aa + aa + a + a) × (aaa − aa)/a + aa + a)/a.
3513 := ((aaa−aa−a−a)×aaa/(a+a+a)−aaa−a−a)/a.
3514 := ((aaa − aa − a − a) × aaa/(a + a + a) − aaa − a)/a.
3515 := ((aaa − aa − a − a) × aaa/(a + a + a) − aaa)/a.
3516 := ((aaa − aa − a − a) × aaa/(a + a + a) − aaa + a)/a.
3517 := ((aa + aa + aa − a) × (aaa − a)/a − a − a − a)/a.
3518 := ((aa + aa + aa − a) × (aaa − a)/a − a − a)/a.
3519 := ((aa + aa + aa − a) × (aaa − a)/a − a)/a.
3520 := (aa + aa + aa − a) × (aaa − a)/(a × a).
3521 := ((aa + aa + aa − a) × (aaa − a)/a + a)/a.
3522 := ((aa + aa + aa − a) × (aaa − a)/a + a + a)/a.
3523 := ((aa + aa + aa − a) × (aaa − a)/a + a + a + a)/a.
3524 := ((aa + aa + aa + a + a) × aaaa/aa − aa)/a.
3525 := ((aa + aa + aa + a + a) × aaaa/aa − aa + a)/a.
3525 := ((aa + aa + aa + a + a) × aaaa/aa − aa + a + a)/a.
3527 := (aaaaaa/(aa + aa − a) × (a + a) − a)/(a + a + a).
3528 := (aaa−aa−a−a)×(aaa−a−a−a)/((a+a+a)×a).
30
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3529 := ((aa + aa + aa − a) × (aaa − a)/a + aa − a − a)/a.
3530 := ((aa + aa + aa − a) × (aaa − a)/a + aa − a)/a.
3531 := ((aa + aa + aa − a) × (aaa − a)/a + aa)/a.
3532 := ((aa + aa + aa − a) × (aaa − a)/a + aa + a)/a.
3533 := ((aa + aa + aa + a + a) × aaaa/aa − a − a)/a.
3534 := ((aa + aa + aa + a + a) × aaaa/aa − a)/a.
3535 := (aa + aa + aa + a + a) × aaaa/(aa × a).
3536 := ((aa + aa + aa + a + a) × aaaa/aa + a)/a.
3537 := ((aa + aa + aa + a + a) × aaaa/aa + a + a)/a.
3538 := ((aa + aa + aa − a) × aaa/a − aa − a − a − a)/a.
3539 := ((aa + aa + aa − a) × aaa/a − aa − a − a)/a.
3540 := ((aa + aa + aa − a) × aaa/a − aa − a)/a.
3541 := ((aa + aa + aa − a) × aaa/a − aa)/a.
3542 := ((aa + aa + aa − a) × aaa/a − aa + a)/a.
3543 := ((aa + aa + aa − a) × aaa/a − aa + a + a)/a.
3544 := (((aaaa + aaa) × (a + a + a) − aa × aa)/a − a)/a.
3545 := ((aaaa + aaa) × (a + a + a) − aa × aa)/(a × a).
3546 := (((aaaa + aaa) × (a + a + a) − aa × aa)/a + a)/a.
3547 := ((aa + aa + aa − a) × aaa/a − a − a − a − a − a)/a.
3548 := ((aa + aa + aa − a) × aaa/a − a − a − a − a)/a.
3549 := ((aa + aa + aa − a) × aaa/a − a − a − a)/a.
3550 := ((aa + aa + aa − a) × aaa/a − a − a)/a.
3551 := ((aa + aa + aa − a) × aaa/a − a)/a.
3552 := (aa + aa + aa − a) × aaa/(a × a).
3553 := ((aa + aa + aa − a) × aaa/a + a)/a.
3554 := ((aa + aa + aa − a) × aaa/a + a + a)/a.
3555 := ((aa + aa + aa − a) × aaa/a + a + a + a)/a.
3556 := ((aa + aa + aa − a) × aaa/a + a + a + a + a)/a.
3557 := ((aa + aa + aa − a) × aaa/a + a + a + a + a + a)/a.
3558 := ((aaaa + a) × aa/(a + a) + aaaa − aaa)/(a + a).
3559 = ((aa + aa + aa − a) × aaa/a + aa − a − a − a − a)/a.
3560 = ((aa + aa + aa − a) × aaa/a + aa − a − a − a)/a.
3561 = ((aa + aa + aa − a) × aaa/a + aa − a − a)/a.
3562 = ((aa + aa + aa − a) × aaa/a + aa − a)/a.
3563 = ((aa + aa + aa − a) × aaa/a + aa)/a.
3564 = ((aa + aa + aa − a) × aaa/a + aa + a)/a.
3565 = ((aa + aa + aa − a) × aaa/a + aa + a + a)/a.
3566 := (((aaa + a) × (aa + a)) + (aaaa × (a + a)))/(a × a).
3567 := ((aa+aa+aa+a+a)×(aaaa+aa)/aa−a−a−a)/a.
3568 := (aaaaa − aaa/(a + a + a) × aa)/(a + a + a).
3569 := ((aa + aa + aa + a + a) × (aaaa + aa)/aa − a)/a.
3570 := (aa + aa + aa + a + a) × (aaaa + aa)/(aa × a).
3571 := ((aa + aa + aa − a) × (aaa + a)/a − aa − a − a)/a.
3572 := ((aa + aa + aa − a) × (aaa + a)/a − aa − a)/a.
3573 := ((aa + aa + aa − a) × (aaa + a)/a − aa)/a.
3574 := ((aa + aa + aa − a) × (aaa + a)/a − aa + a)/a.
3575 := (aaaa − aa) × (aa + a + a)/((a + a) × (a + a)).
3576 := ((aaaa − aa) × (aa + a + a)/(a + a) + a + a)/(a + a).
3577 := ((aaa−aa−a−a−a)×aaa/(a+a+a)−aa−a)/a.
3578 := ((aaa − aa − a − a − a) × aaa/(a + a + a) − aa)/a.
3579 := ((aaa−aa−a−a−a)×aaa/(a+a+a)−aa+a)/a.
3580 := ((aaaa − aa) × aa/(a + a) + aaaa − a)/(a + a).
3581 := ((aaaa − aa) × aa/(a + a) + aaaa + a)/(a + a).
3582 := ((aa + aa + aa − a) × (aaa + a)/a − a − a)/a.
3583 := ((aa + aa + aa − a) × (aaa + a)/a − a)/a.
3584 := (aa + aa + aa − a) × (aaa + a)/(a × a).
3585 := ((aa + aa + aa − a) × (aaa + a)/a + a)/a.
3586 := ((aa + aa + aa − a) × (aaa + a)/a + a + a)/a.
3587 := ((aaa − aa − a − a − a) × aaa/(a + a + a) − a − a)/a.
3588 := ((aaa − aa − a − a − a) × aaa/(a + a + a) − a)/a.
3589 := (aaa − aa − a − a − a) × aaa/((a + a + a) × a).
3590 := ((aaa − aa − a − a − a) × aaa/(a + a + a) + a)/a.
3591 := ((aaa − aa − a − a − a) × aaa/(a + a + a) + a + a)/a.
3592 := ((aaa−aa−a−a−a)×aaa/(a+a+a)+a+a+a)/a.
3593 := ((aaaaa + a) × aa/(aa + aa + aa) − aaa)/a.
3594 := ((aaaaa + a) × aa/(aa + aa + aa) − aaa + a)/a.
3595 := ((aa + aa + aa) × (aaa − a − a)/a − a − a)/a.
3596 := ((aa + aa + aa) × (aaa − a − a)/a − a)/a.
3597 := (aa + aa + aa) × (aaa − a − a)/(a × a).
3598 := ((aa + aa + aa) × (aaa − a − a)/a + a)/a.
3599 := ((aa + aa + aa) × (aaa − a − a)/a + a + a)/a.
3600 := (aaa − a − a − a) × (aaa − aa)/((a + a + a) × a).
3601 := (aaaa−a−a−a)×(aa+a+a)/((a+a+a+a)×a).
3602 := ((aaa − a − a − a − a) × aaaa/aa − a)/(a + a + a).
3603 := (aaaaa + a)/(a + a + a) − aaaa/aa.
3604 := (aaaaa + a)/(a + a + a) − (aaaa − aa)/aa.
3605 := ((aa + aa + aa − a) × (aaa + a + a)/a − aa)/a.
3606 := (aaaaa + aa − a)/(a + a + a) − aaaa/aa.
3607 := ((aaaa − a) × (aa + a + a)/(a + a) − a)/(a + a).
3608 := ((aaaa − a) × (aa + a + a)/(a + a) + a)/(a + a).
3609 := ((aaaa − a) × aa/(a + a) + aaaa + a + a)/(a + a).
3610 := ((aaaa + aaa) × (aa + a)/(a + a) − aaa − a)/(a + a).
3611 := (aaaaa − aaa + a)/(a + a + a) − (aaa + a)/(a + a).
3612 := (aaaaa − aaa + a)/(a + a + a) − (aaa − a)/(a + a).
3613 := ((aaaa − a) × (aa + a + a)/(a + a) + aa)/(a + a).
3614 := (aaaa + a) × (aa + a + a)/((a + a) × (a + a)).
3615 := ((aaaa + a) × (aa + a + a)/(a + a) + a + a)/(a + a).
3616 := (aa + aa + aa − a) × (aaa + a + a)/(a × a).
3617 := ((aa + aa + aa − a) × (aaa + a + a)/a + a)/a.
3618 := ((aa + aa + aa − a) × (aaa + a + a)/a + a + a)/a.
3619 := ((aaaa + a) × aa/(a + a) + aaaa + aa)/(a + a).
3620 := ((aaaa + a) × (aa + a + a)/(a + a) + aa + a)/(a + a).
3621 := ((aaaa + aaa − aa) × (a + a + a)/a − aa − a)/a.
3622 := ((aaaa + aaa − aa) × (a + a + a)/a − aa)/a.
3623 := ((aaaa + aaa − aa) × (a + a + a)/a − aa + a)/a.
3624 := (aaaa × (a + a + a)/aa − a) × (aa + a)/(a × a).
3625 := ((aaa − aa − a − a) × aaa/(a + a + a) − a)/a.
3626 := (aaa − aa − a − a) × aaa/((a + a + a) × a).
3627 := (aaaa × aaa/(aa + aa + aa) − aaa + a)/a.
3628 := (aaaa × aaa/(aa + aa + aa) − aaa + a + a)/a.
3629 := ((aa + aa + aa) × (aaa − a)/a − a)/a.
3630 := (aa + aa + aa) × (aaa − a)/(a × a).
3631 := ((aa + aa + aa) × (aaa − a)/a + a)/a.
3632 := ((aa + aa + aa) × (aaa − a)/a + a + a)/a.
3633 := (aaaa + aaa − aa) × (a + a + a)/(a × a).
3634 := ((aaaa + aaa − aa) × (a + a + a)/a + a)/a.
3635 := ((aaaa + aaa − aa) × (a + a + a)/a + a + a)/a.
3636 := aaaa × (a + a + a) × (aa + a)/(aa × a × a).
3637 := (aaaa × (a + a + a) × (aa + a)/(aa × a) + a)/a.
3638 := (aaa−a−a−a−a)×(aaaa+aa)/((a+a+a)×aa).
3639 := (aaaaa − aa)/(a + a + a) − (aaa + aa)/(a + a).
3640 := ((aaaa + aa) × aa/(a + a) + aaaa − a − a)/(a + a).
3641 := ((aaaa + aa) × aa/(a + a) + aaaa)/(a + a).
3642 := ((aaaa + aa) × aa/(a + a) + aaaa + a + a)/(a + a).
3643 := (aaaaa + a)/(a + a + a) − (aaa + aa)/(a + a).
3644 := (aaaaa − aa)/(a + a + a) − (aaa + a)/(a + a).
3645 := (aaaaa − aa)/(a + a + a) − (aaa − a)/(a + a).
3646 := ((aa + aa + aa + a + a) × aaaa/aa + aaa)/a.
3647 := (aaaa × (a + a + a) × (aa + a)/(aa × a) + aa)/a.
3648 := (aaaa × (a + a + a)/aa + a) × (aa + a)/(a × a).
3649 := (aaaaa + a)/(a + a + a) − (aaa − a)/(a + a).
3650 := ((aaa + aaa + aaa − a) × aa/a − a − a)/a.
3651 := ((aaa + aaa + aaa − a) × aa/a − a)/a.
3652 := (aaa + aaa + aaa − a) × aa/(a × a).
3653 := ((aaa + aaa + aaa − a) × aa/a + a)/a.
3654 := ((aaa + aaa + aaa − a) × aa/a + a + a)/a.
3655 := ((aaa + aaa + aaa − a) × aa/a + a + a + a)/a.
3656 := (aaaaa − aaa − aa − aa − aa + a)/(a + a + a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3657 := (aaaa + aaa − a − a − a) × (a + a + a)/(a × a).
3658 := ((aaaa + aaa − a − a − a) × (a + a + a)/a + a)/a.
3659 := (aaaaa − aaa − aa − aa − a)/(a + a + a).
3660 := ((aa + aa + aa) × aaa/a − a − a − a)/a.
3661 := ((aa + aa + aa) × aaa/a − a − a)/a.
3662 := ((aa + aa + aa) × aaa/a − a)/a.
3663 := (aa + aa + aa) × aaa/(a × a).
3664 := ((aa + aa + aa) × aaa/a + a)/a.
3665 := ((aa + aa + aa) × aaa/a + a + a)/a.
3666 := (aaaa + aaa) × (a + a + a)/(a × a).
3667 := (aaaaa − aaa + a)/(a + a + a).
3668 := (aaaaa − aaa + a)/(a + a + a) + a/a.
3669 := (aaaa + aaa + a) × (a + a + a)/(a × a).
3670 := ((aaaa + aaa + a) × (a + a + a)/a + a)/a.
3671 := (aaaaa − aaa + aa + a + a)/(a + a + a).
3672 := (aaaa + aaa + a + a) × (a + a + a)/(a × a).
3673 := ((aaa + aaa + aaa + a) × aa/a − a)/a.
3674 := (aaa + aaa + aaa + a) × aa/(a × a).
3675 := ((aaa + aaa + aaa + a) × aa/a + a)/a.
3676 := ((aaa + aaa + aaa + a) × aa/a + a + a)/a.
3677 := ((aaaa + aaa) × (aa + aa + aa)/aa + aa)/a.
3678 := (aaaaa − aaa + aa + aa + aa + a)/(a + a + a).
3679 := ((aaaa + aaa + a) × (a + a + a)/a + aa − a)/a.
3680 := ((aaaa + aaa + a) × (a + a + a)/a + aa)/a.
3681 := ((aaaa + aaa + a) × (a + a + a)/a + aa + a)/a.
3682 := ((aaaa + aaa + a) × (a + a + a)/a + aa + a + a)/a.
3683 := ((aaa + aaa + aaa + a + a) × aa/a − a − a)/a.
3684 := ((aaa + aaa + aaa + a + a) × aa/a − a)/a.
3685 := (aaa + aaa + aaa + a + a) × aa/(a × a).
3686 := ((aaa + aaa + aaa + a + a) × aa/a + a)/a.
3687 := ((aaa + aaa + aaa + a + a) × aa/a + a + a)/a.
3688 := (aaaaa − aa − aa − aa − aa)/(a + a + a) − a/a.
3689 := (aaaaa − aa − aa − aa − aa)/(a + a + a).
3690 := (aaaa − a − a − a − a) × (aa − a)/((a + a + a) × a).
3691 := ((aaaa + aaa + a) × (a + a + a)/a + aa + aa)/a.
3692 := (aaaaa − aa − aa − aa − a − a)/(a + a + a).
3693 := (aaaaa − aa − aa − aa + a)/(a + a + a).
3694 := ((aa + aa + aa) × (aaa + a)/a − a − a)/a.
3695 := ((aa + aa + aa) × (aaa + a)/a − a)/a.
3696 := (aa + aa + aa) × (aaa + a)/(a × a).
3697 := ((aa + aa + aa) × (aaa + a)/a + a)/a.
3698 := (aaaaa − aa)/(a + a + a) − (a + a)/a.
3699 := (aaaaa − aa)/(a + a + a) − a/a.
3700 := (aaaaa − aa)/(a + a + a).
3701 := ((aaaaa − aa)/(a + a + a) × a + a)/a.
3702 := (aaaa + aaa + aa + a) × (a + a + a)/(a × a).
3703 := (aaaaa − a − a)/(a + a + a).
3704 := (aaaaa + a)/(a + a + a).
3705 := ((aaaaa + a)/(a + a + a) × a + a)/a.
3706 := (aaaaa + aa − a − a − a − a)/(a + a + a).
3707 := (aaaaa + aa − a)/(a + a + a).
3708 := (aaaaa + aa + a + a)/(a + a + a).
3709 := (aaaaa + a)/(a + a + a) + (aa − a)/(a + a).
3710 := (aaaa + a + a) × (aa − a)/((a + a + a) × a).
3711 := (aaaaa + aa + aa)/(a + a + a).
3712 := (aaaaa + aa + aa + a + a + a)/(a + a + a).
3713 := (aaaaa + aa − a)/(a + a + a) + (aa + a)/(a + a).
3714 := (aaaaa + a)/(a + a + a) + (aaa − a)/aa.
3715 := (aaaaa + aa + aa + aa + a)/(a + a + a).
3716 := ((aaa + aa) × (aaa + aa)/(a + a) − aa + a)/(a + a).
3717 := (aaaaa + aa − a)/(a + a + a) + (aaa − a)/aa.
3718 := (aaaaa + aa + aa + aa + aa − a)/(a + a + a).
3719 := (aaaaa + aa + aa + aa + aa + a + a)/(a + a + a).
3720 := ((aaa + aa) × (aaa + aa)/(a + a) − a − a)/(a + a).
31
3721 := (aaa + aa) × (aaa + aa)/((a + a) × (a + a)).
3722 := ((aaa + aa) × (aaa + aa)/(a + a) + a + a)/(a + a).
3723 := (aaaaa − aaa + a)/(a + a + a) + (aaa + a)/(a + a).
3724 := (aaa + aa + aa) × (aaa + a)/((a + a + a + a) × a).
3725 := ((aaaa × aaa)/(aa + aa + aa) − aa − a)/a.
3726 := ((aaaa × aaa)/(aa + aa + aa) − aa)/a.
3727 := (aaaa × aaa/(a + a + a) − aaa + a)/aa.
3728 := ((aa + aa + aa) × (aaa + a + a)/a − a)/a.
3729 := (aa + aa + aa) × (aaa + a + a)/(a × a).
3730 := (aaaa × aaa/aa − aa − aa + a)/(a + a + a).
3731 := aaaa × aaa/((a + a + a) × aa) − (aa + a)/(a + a).
3732 := (aaaa + aaa + aa + aa) × (a + a + a)/(a × a).
3733 := (aaaaa + aaa − aa − aa − a)/(a + a + a).
3734 := ((aaaa × aaa)/aa − aa + a + a)/(a + a + a).
3735 := (aaaa × aaa/(aa + aa + aa) − a − a)/a.
3736 := (aaaa × aaa/(a + a + a) − aa)/aa.
3737 := aaaa × aaa/((a + a + a) × aa).
3738 := (aaaa × aaa/(a + a + a) + aa)/aa.
3739 := (aaaa × aaa/(aa + aa + aa) + a + a)/a.
3740 := (aa + aa + aa + a) × (aaa − a)/(a × a).
3741 := (aaaaa + aaa + a)/(a + a + a).
3742 := (aaaaa + aaa + a + a + a + a)/(a + a + a).
3743 := (aaaaa + aaa + a)/(a + a + a) + (a + a)/a.
3744 := (aaaaa + aaa + aa − a)/(a + a + a).
3745 := (aaaaa + aaa + aa + a + a)/(a + a + a).
3746 := (aaaa × aaa/(a + a + a) + aaa − a − aa)/aa.
3747 := (aaaa × aaa/(a + a + a) + aaa − a)/aa.
3748 := (aaaaa + aaa + aa + aa)/(a + a + a).
3749 := (aaaa × aaa/(aa + aa + aa) + aa + a)/a.
3750 := (aaaa × aaa/(aa + aa + aa) + aa + a + a)/a.
3751 := (aaaaa + aaa + a)/(a + a + a) + (aa − a)/a.
3752 := (aaaaa + aaa + a)/(a + a + a) + aa/a.
3753 := (aaaaa + aaa + a)/(a + a + a) + (aa + a)/a.
3754 := (aaaaa + a)/(a + a + a) + (aaa − aa)/(a + a).
3755 := (aaaaa − aa)/(a + a + a) + (aaa − a)/(a + a).
3756 := (aaaa/aa × (a + a) + aaa) × (aa + a)/(a × a).
3757 := (aaaaa + aa − a)/(a + a + a) + (aaa − aa)/(a + a).
3758 := ((aaaa − a) × (aaa + aa)/(aa + a) − aa)/(a + a + a).
3759 := (aaaaa + a)/(a + a + a) + (aaa − a)/(a + a).
3760 := (aaaaa + a)/(a + a + a) + (aaa + a)/(a + a).
3761 := ((aa + aa + aa + a) × aaa/a − aa − a − a)/a.
3762 := ((aa + aa + aa + a) × aaa/a − aa − a)/a.
3763 := ((aa + aa + aa + a) × aaa/a − aa)/a.
3764 := ((aa + aa + aa + a) × aaa/a − aa + a)/a.
3765 := ((aa + aa + aa + a) × aaa/a − aa + a + a)/a.
3766 := ((aa + aa + aa + a) × aaa/a − aa + a + a + a)/a.
3767 := ((aaa + a) × aaaa/aa − aa)/(a + a + a).
3768 := (aaaa × (a + a + a)/aa + aa) × (aa + a)/(a × a).
3769 := ((aa + aa + aa + a) × aaa/a − a − a − a − a − a)/a.
3770 := ((aaa + a) × aaaa/aa − a − a)/(a + a + a).
3771 := ((aaa + a) × aaaa/aa + a)/(a + a + a).
3772 := ((aa + aa + aa + a) × aaa/a − a − a)/a.
3773 := ((aa + aa + aa + a) × aaa/a − a)/a.
3774 := (aa + aa + aa + a) × aaa/(a × a).
3775 := ((aa + aa + aa + a) × aaa/a + a)/a.
3776 := ((aa + aa + aa + a) × aaa/a + a + a)/a.
3777 := (aaaaa + aaa + aaa − a − a)/(a + a + a).
3778 := (aaaaa + aaa + aaa + a)/(a + a + a).
3779 := (aaaaa + aaa + aaa + a + a + a + a)/(a + a + a).
3780 := (aaaa + aa + aa + a) × (aa − a)/((a + a + a) × a).
3781 := (aaaaa + aaa + aaa + aa − a)/(a + a + a).
3782 := (aa + aa + aa − a − a) × (aaa + aa)/(a × a).
3783 := ((aaa + aaa + aaa + aa) × aa/a − a)/a.
3784 := (aaa + aaa + aaa + aa) × aa/(a × a).
32
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3785 := (aaaaa + aaa + aaa + aa + aa)/(a + a + a).
3786 := ((aaa + aaa + aaa + aa) × aa/a + a + a)/a.
3787 := ((aaa + aaa + aaa + aa) × aa/a + a + a + a)/a.
3788 := (aaaaaa × (a + a + a)/aa + a)/(aa − a − a − a).
3789 := (((aaaa+aaa+a)×(a+a+a)+(aa×aa))/a−a)/a.
3790 := ((aaaa + aaa + a) × (a + a + a) + aa × aa)/(a × a).
3791 := (((aaaa+aaa+a)×(a+a+a)+aa×aa)/a+a)/a.
3792 := aaaa × aaa/((a + a + a) × aa) + (aaa − a)/(a + a).
3793 := aaaa × aaa/((a + a + a) × aa) + (aaa + a)/(a + a).
3794 := ((aaa + aaa + aaa + aa) × aa/a + aa − a)/a.
3795 := ((aaa + aaa + aaa + aa) × aa/a + aa)/a.
3796 := ((aaa + aa + a) × aaaa/(a + a + a) + a)/(aa + a).
3797 := ((aaa + a + a) × aaaa/aa − aa − aa)/(a + a + a).
3798 := ((aa + aa + aa + a) × (aaa + a)/a − aa + a)/a.
3799 := ((aaaa + a) × aaa/(aa + a) + aaaa)/(a + a + a).
3800 := (aaa + a + a + a) × (aaa − aa)/((a + a + a) × a).
3801 := ((aaa + a + a) × (aaaa − a)/(a + a + a) + a)/aa.
3802 := (aaaaa + a)/(a + a + a) + (aaa − aa − a − a)/a.
3803 := (aaaaa + a)/(a + a + a) + (aaa − aa − a)/a.
3804 := ((aaa + a + a) × aaaa/aa − a)/(a + a + a).
3805 := (aaaaa + a)/(a + a + a) + aaaa/aa.
3806 := ((aa + aa + aa + a) × (aaa + a)/a − a − a)/a.
3807 := ((aa + aa + aa + a) × (aaa + a)/a − a)/a.
3808 := (aa + aa + aa + a) × (aaa + a)/(a × a).
3809 := ((aa + aa + aa + a) × (aaa + a)/a + a)/a.
3809 := ((aa + aa + aa + a) × (aaa + a)/a + a + a)/a.
3811 := (aaaa + aa + aa) × aaa/((a + a + a) × aa).
3812 := (aaaaa + a)/(a + a + a) + (aaa − a − a − a)/a.
3813 := (aaaaa + a)/(a + a + a) + (aaa − a − a)/a.
3814 := (aaaaa + a)/(a + a + a) + (aaa − a)/a.
3815 := (aaaaa + a)/(a + a + a) + aaa/a.
3816 := (aaaaa + a)/(a + a + a) + (aaa + a)/a.
3817 := (aaaaa + a)/(a + a + a) + (aaa + a + a)/a.
3818 := (aaaaa + a)/(a + a + a) + (aaa + a + a + a)/a.
3819 := ((aa + aa + aa + a) × (aaa + a)/a + aa)/a.
3820 := ((aa + aa + aa + a) × (aaa + a)/a + aa + a)/a.
3821 := ((aa + aa + aa + a) × (aaa + a)/a + aa + a + a)/a.
3822 := (aaaaa+a)/(a+a+a)+(aaa+aa−a−a−a−a)/a.
3823 := (aaaaa + a)/(a + a + a) + (aaa + aa − a − a − a)/a.
3824 := (aaaaa + a)/(a + a + a) + (aaa + aa − a − a)/a.
3825 := (aaaaa + a)/(a + a + a) + (aaa + aa − a)/a.
3826 := (aaaaa + a)/(a + a + a) + (aaa + aa)/a.
3827 := (aaaaa + a)/(a + a + a) + (aaa + aa + a)/a.
3828 := (aaaaa + a)/(a + a + a) + (aaa + aa + a + a)/a.
3829 := (aaaaa + a)/(a + a + a) + (aaa + aa + a + a + a)/a.
3830 := ((aa + aa + aa + a) × (aaa + a + a)/a − aa − a)/a.
3831 := ((aa + aa + aa + a) × (aaa + a + a)/a − aa)/a.
3832 := ((aa + aa + aa + a) × (aaa + a + a)/a − aa + a)/a.
3833 := ((aaaa−aaa)×(aa+aa+a)/(a+a)−a)/(a+a+a).
3834 := ((aaa + a + a + a) × aaaa/aa − aa − a)/(a + a + a).
3835 := (aaaa × aaa/(aa + aa + aa) + aaa − aa − a − a)/a.
3836 := (aaaa × aaa/(aa + aa + aa) + aaa − aa − a)/a.
3837 := (aaaa × aaa/(a + a + a) + aaaa − aa)/aa.
3838 := (aaa + a + a + a) × aaaa/(aa × (a + a + a)).
3839 := (aaa/(a + a + a) × aa + aaaaa − a)/(a + a + a).
3840 := (aaa/(a + a + a) × aa + aaaaa + a + a)/(a + a + a).
3841 := ((aaa + a + a) × aaaa/aa + aaa − a)/(a + a + a).
3842 := (aa + aa + aa + a) × (aaa + a + a)/(a × a).
3843 := ((aa + aa + aa + a) × (aaa + a + a)/a + a)/a.
3844 := ((aa + aa + aa + a) × (aaa + a + a)/a + a + a)/a.
3845 := ((aaaa + aa) × (aaa + a)/aa + aaa)/(a + a + a).
3846 := (aaaa × aaa/(aa + aa + aa) + aaa − a − a)/a.
3847 := (aaaa × aaa/(aa + aa + aa) + aaa − a)/a.
3848 := (aaaa × aaa/(aa + aa + aa) + aaa)/a.
3849 := (aaaa × aaa/(aa + aa + aa) + aaa + a)/a.
3850 := (aa + aa + aa + a + a) × (aaa − a)/(a × a).
3851 := ((aa + aa + aa + a + a) × (aaa − a)/a + a)/a.
3852 := ((aa + aa + aa + a + a) × (aaa − a)/a + a + a)/a.
3853 := ((aa + aa + aa + a + a) × (aaa − a)/a + a + a + a)/a.
3854 := ((aa+aa+aa+a+a)×(aaa−a)/a+a+a+a+a)/a.
3855 := ((aaaa − aa) × (aa + a)/(a + a) + aaaa − a)/(a + a).
3856 := ((aaa + aaa + aaa − aa) × (aa + a)/a + a + a +
a − aa)/a.
3857 := (aaaa − aa + a + a) × (aa + a + a + a)/((a + a +
a + a) × a).
3858 := ((aa+aa+aa+a+a)×(aaa−a)/a+aa−a−a−a)/a.
3859 := ((aa+aa+aa+a+a)×(aaa−a)/a+aa−a−a)/a.
3860 := ((aa + aa + aa + a + a) × (aaa − a)/a + aa − a)/a.
3861 := ((aa + aa + aa + a + a) × (aaa − a)/a + aa)/a.
3862 := ((aaa + aaa + aaa − aa) × (aa + a)/a − a − a)/a.
3863 := ((aaa + aaa + aaa − aa) × (aa + a)/a − a)/a.
3864 := (aaa + aaa + aaa − aa) × (aa + a)/(a × a).
3865 := ((aaa + aaa + aaa − aa) × (aa + a)/a + a)/a.
3866 := ((aaa + aaa + aaa − aa) × (aa + a)/a + a + a)/a.
3867 := ((aaa + aaa + aaa − aa) × (aa + a)/a + a + a + a)/a.
3868 := ((aa−aaa−aaa)×(a−aaa)/(a+a)−a)/(a+a+a).
3869 := ((aa + aa + aa + a + a) × aaa/a − aa − a − a −
a − a − a)/a.
3870 := ((aa+aa+aa+a+a)×aaa/a−aa−a−a−a−a)/a.
3871 := ((aa + aa + aa + a + a) × aaa/a − aa − a − a − a)/a.
3872 := ((aa + aa + aa + a + a) × aaa/a − aa − a − a)/a.
3873 := ((aa + aa + aa + a + a) × aaa/a − aa − a)/a.
3874 := ((aa + aa + aa + a) × aaa/a − aa + aaa)/a.
3875 := ((aa + aa + aa + a) × (aaa + a + a + a)/a − a)/a.
3876 := (aa + aa + aa + a) × (aaa + a + a + a)/(a × a).
3877 := ((aa + aa + aa + a) × (aaa + a + a + a)/a + a)/a.
3878 := (aaaa−a−a−a)×(aa+a+a+a)/((a+a+a+a)×a).
3879 := (aa+aa+aa+a+a)×aaa/(a×a)−(aa+a)/(a+a).
3880 := (aa+aa+aa+a+a)×aaa/(a×a)−(aa−a)/(a+a).
3881 := ((aa + aa + aa + a + a) × aaa/a − a − a − a − a)/a.
3882 := ((aa + aa + aa + a + a) × aaa/a − a − a − a)/a.
3883 := ((aa + aa + aa + a + a) × aaa/a − a − a)/a.
3884 := ((aa + aa + aa + a + a) × aaa/a − a)/a.
3885 := (aa + aa + aa + a + a) × aaa/(a × a).
3886 := ((aa + aa + aa + a + a) × aaa/a + a)/a.
3887 := ((aa + aa + aa + a + a) × aaa/a + a + a)/a.
3888 := ((aa + aa − a) × aaaa/(a + a + a) − a)/(a + a).
3889 := ((aa+aa+aa+a)×(aaa+a+a+a)/a+aa+a+a)/a.
3890 := (aa+aa+aa+a+a)×aaa/(a×a)+(aa−a)/(a+a).
3891 := (aa+aa+aa+a+a)×aaa/(a×a)+(aa+a)/(a+a).
3892 := (aa + aa − a) × (aaaa + a)/(a + a + a)/(a + a).
3893 := ((aa + aa + aa + a + a) × aaa/a + aa − a − a − a)/a.
3894 := ((aa + aa + aa + a + a) × aaa/a + aa − a − a)/a.
3895 := ((aa + aa + aa + a + a) × aaa/a + aa − a)/a.
3896 := ((aa + aa + aa + a + a) × aaa/a + aa)/a.
3897 := ((aa + aa + aa + a + a) × aaa/a + aa + a)/a.
3898 := ((aa + aa + aa + a + a) × aaa/a + aa + a + a)/a.
3899 := ((aa + aa + aa + a + a) × aaa/a + aa + a + a + a)/a.
3900 := (aaa − aa − aa − aa) × (aaa − aa)/((a + a) × a).
3901 := ((aaa − aa − aa − aa) × (aaa − aa)/(a + a) + a)/a.
3902 := ((aaa−aa−aa−aa)×(aaa−aa)/(a+a)+a+a)/a.
3903 := ((aaa + aaa − aa) × aaa/(a + a + a) − a)/(a + a).
3904 := (aa + aa + aa − a) × (aaa + aa)/(a × a).
3905 := ((aaa + aa) × (aa + aa) + aaa × aa)/(a × a).
3906 := ((aaa−a)×aa/(a+a)+aaaaa+a+a)/(a+a+a).
3907 := ((aa+aa+aa+a+a)×(aaa+a)/a−aa−a−a)/a.
3908 := ((aa + aa + aa + a + a) × (aaa + a)/a − aa − a)/a.
3909 := ((aaa + a)/(a + a) × aa + aaaaa)/(a + a + a).
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
3910 := ((aaa − a − a) × aaa/(a + a + a) − aaa − aa − a)/a.
3911 := ((aaa − a − a) × aaa/(a + a + a) − aaa − aa)/a.
3912 := (aaaa − aaa − aa − aa) × (aa + a)/((a + a + a) × a).
3913 := ((aaaa×(a+a+a)+aaa×aaa)/(a+a)−a)/(a+a).
3914 := ((aaaa×(a+a+a)+aaa×aaa)/(a+a)+a)/(a+a).
3915 := ((aa + aa + aa − a) × (aaa + aa)/a + aa)/a.
3916 := ((aaaa + aaa)/(a + a) × aa + aaaa)/(a + a).
3917 := ((aa + aa + aa + a + a) × (aaa + a)/a − a − a − a)/a.
3918 := ((aa + aa + aa + a + a) × (aaa + a)/a − a − a)/a.
3919 := ((aa + aa + aa + a + a) × (aaa + a)/a − a)/a.
3920 := (aa + aa + aa + a + a) × (aaa + a)/(a × a).
3921 := ((aaa − a − a) × aaa/(a + a + a) − aaa − a)/a.
3922 := ((aaa − a − a) × aaa/(a + a + a) − aaa)/a.
3923 := ((aaa − a − a) × aaa/(a + a + a) − aaa + a)/a.
3924 := (aaa − a − a − a) × (aaa − a − a)/((a + a + a) × a).
3925 := ((aaa − a − a − a) × (aaa − a − a)/(a + a + a) + a)/a.
3926 := (aaa × (aa + a)/(a + a) + aaaaa + a)/(a + a + a).
3927 := (aaaa + aa) × (aa + aa − a)/((a + a) × (a + a + a)).
3928 := ((aaa+a)×(aa+a)/(a+a)+aaaaa+a)/(a+a+a).
3929 := ((aa+aa+aa+a+a)×(aaa+a)/a+aa−a−a)/a.
3930 := ((aa + aa + aa + a + a) × (aaa + a)/a + aa − a)/a.
3931 := ((aa + aa + aa + a + a) × (aaa + a)/a + aa)/a.
3932 := ((aa + aa + aa + a + a) × (aaa + a)/a + aa + a)/a.
3933 := ((aa+aa+aa+a+a)×(aaa+a)/a+aa+a+a)/a.
3934 := ((aa + aa + aa − a) × (aaa + aa + a)/a − a − a)/a.
3935 := ((aa + aa + aa − a) × (aaa + aa + a)/a − a)/a.
3936 := (aa + aa + aa − a) × (aaa + aa + a)/(a × a).
3937 := ((aa + aa + aa − a) × (aaa + aa + a)/a + a)/a.
3938 := ((aa + aa + aa − a) × (aaa + aa + a)/a + a + a)/a.
3939 := aaaa × (aa + a + a) × (a + a + a)/(aa × a × a).
3940 := (aaaa × (aa + a + a) × (a + a + a)/(aa × a) + a)/a.
3941 := ((aaa + aa) × aaa/(a + a) + aaaa)/(a + a).
3942 := (aaaa × (aa + a + a)/aa + a) × (a + a + a)/(a × a).
3943 := ((aaaa × (aa + a + a)/aa + a) × (a + a + a)/a + a)/a.
3944 := ((aa + aa + aa + a + a) × (aaa + a + a)/a − aa)/a.
3945 := ((aa+aa+aa+a+a)×(aaa+a+a)/a−aa−a)/a.
3946 := ((aaaa − a)/(a + a + a) × aa − aaa − aa − a − a)/a.
3947 := ((aaaa − a)/(a + a + a) × aa − aaa − aa − a)/a.
3948 := ((aaaa − aa − aa − aa − a) × aa/(a + a + a) − a)/a.
3949 := (aaaa − aa − aa − aa − a) × aa/((a + a + a) × a).
3950 := ((aaaa − aa − aa − aa − a) × aa/(a + a + a) + a)/a.
3951 := ((aaaa−aaa−aa−a)×(aa+a)/(a+a+a)−a)/a.
3952 := (aaaa − aaa − aa − a) × (aa + a)/((a + a + a) × a).
3953 := ((aa + aa + aa + a + a) × (aaa + a + a)/a − a − a)/a.
3954 := ((aa + aa + aa + a + a) × (aaa + a + a)/a − a)/a.
3955 := (aa + aa + aa + a + a) × (aaa + a + a)/(a × a).
3956 := (aaaa − aaa − aa) × (aa + a)/((a + a + a) × a).
3957 := ((aaaa − a)/(a + a + a) × aa − aaa − a − a)/a.
3958 := ((aaaa − a)/(a + a + a) × aa − aaa − a)/a.
3959 := ((aaaa − a)/(a + a + a) × aa − aaa)/a.
3960 := (aaa − a − a − a) × (aaa − a)/((a + a + a) × a).
3961 := ((aaa − a − a − a) × (aaa − a)/(a + a + a) + a)/a.
3962 := ((aaa − a − a − a) × (aaa − a)/(a + a + a) + a + a)/a.
3963 := ((aaa−a−a−a)×(aaa−a)/(a+a+a)+a+a+a)/a.
3964 := ((aaaa + aaa + aaa − aa) × (a + a + a)/a − a − a)/a.
3965 := ((aaaa + aaa + aaa − aa) × (a + a + a)/a − a)/a.
3966 := (aaaa + aaa + aaa − aa) × (a + a + a)/(a × a).
3967 := (aaaaaa × (aa + a)/aaa − aaa)/(a + a + a).
3968 := (aaa + aa + a + a) × (aa + aa + aa − a)/(a × a).
3969 := ((aaa + aa + a + a) × (aa + aa + aa − a)/a + a)/a.
3970 := ((aaa + aaa + aaa − a − a) × (aa + a)/a − a − a)/a.
3971 := ((aaa + aaa + aaa − a − a) × (aa + a)/a − a)/a.
3972 := (aaa + aaa + aaa − a − a) × (aa + a)/(a × a).
3973 := ((aaa + aaa + aaa − a − a) × (aa + a)/a + a)/a.
33
3974 := (aaa/(a + a + a) × aaa − aa − aa − aaa)/a.
3975 := (aaa/(a + a + a) × aaa − aa − aa − aaa + a)/a.
3976 := (aaa/(a + a + a) × aaa − aa − aa − aaa + a + a)/a.
3977 := (aaa/(a+a+a)×aaa−aa−aa−aaa+a+a+a)/a.
3978 := ((aaaaa − aaa) × (a + a)/aa − aa) × (a + a)/(a × a).
3979 := ((aaaa−aaa)×(aa+a)/(a+a+a)−aa−aa+a)/a.
3980 := (aaaaaa/aaa × (a + a) − aa − a) × (a + a)/(a × a).
3981 := ((aaa + aaa + aaa − a) × (aa + a)/a − a − a − a)/a.
3982 := ((aaa + aaa + aaa − a) × (aa + a)/a − a − a)/a.
3983 := ((aaa + aaa + aaa − a) × (aa + a)/a − a)/a.
3984 := (aaa + aaa + aaa − a) × (aa + a)/(a × a).
3985 := ((aaa + aaa + aaa − a) × (aa + a)/a + a)/a.
3986 := ((aaa + aaa + aaa − a) × (aa + a)/a + a + a)/a.
3987 := ((aaa + aaa + aaa − a) × (aa + a)/a + a + a + a)/a.
3988 := (aaaa−aaa−a−a−a)×(aa+a)/((a+a+a)×a).
3989 := ((aaaa − aaa) × (aa + a)/(a + a + a) − aa)/a.
3990 := ((aaaa − aa − aa) × aa/(a + a + a) − a − a − a)/a.
3991 := ((aaaa − aa − aa) × aa/(a + a + a) − a − a)/a.
3992 := ((aaaa − aa − aa) × aa/(a + a + a) − a)/a.
3993 := (aaaa − aa − aa) × aa/((a + a + a) × a).
3994 := ((aaaa − aa − aa) × aa/(a + a + a) + a)/a.
3995 := ((aaa − a − a − a) × aaa/(a + a + a) − a)/a.
3996 := (aaa − a − a − a) × aaa/((a + a + a) × a).
3997 := ((aaa − a − a − a) × aaa/(a + a + a) + a)/a.
3998 := ((aaa − a − a − a) × aaa/(a + a + a) + a + a)/a.
3999 := (aaaa + aaa + aaa) × (a + a + a)/(a × a).
4000 := (aaaa − aaa) × (aa + a)/((a + a + a) × a).
4001 := ((aaaa − aaa) × (aa + a)/(a + a + a) + a)/a.
4002 := (aaaaaa/aaa × (a + a) − a) × (a + a)/(a × a).
4003 := (aaaaaa × (aa − a − a − a)/aaa − a − a)/(a + a).
4004 := aaaaaa × (aa + a)/(aaa × (a + a + a)).
4005 := (aaaaaa × (aa + a)/aaa + a + a + a)/(a + a + a).
4006 := (aaaaaa/aaa × (a + a) + a) × (a + a)/(a × a).
4007 := ((aa − aaa) × (a + a) + aaaa × aa)/((a + a + a) × a).
4008 := (aaa + aaa + aaa + a) × (aa + a)/(a × a).
4009 := ((aaa + aaa + aaa + a) × (aa + a)/a + a)/a.
4010 := ((aaa + aaa + aaa + a) × (aa + a)/a + a + a)/a.
4011 := ((aaa + aaa + aaa + a) × (aa + a)/a + a + a + a)/a.
4012 := (aaaa−aaa+a+a+a)×(aa+a)/((a+a+a)×a).
4013 := ((aaaaa+a)×(aa+a+a)/(aa+a)+a)/(a+a+a).
4014 := (aaaa−aaa+a+a+a+a)×(aa+a)/((a+a+a)×a).
4015 := ((aa + aa + aa) × (aaa + aa)/a − aa)/a.
4016 := ((aa + aa + aa) × (aaa + aa)/a − aa + a)/a.
4017 := ((aaa−aa−a−a)×(aaa+aa+a)/(a+a+a)−a)/a.
4018 := (aaa−aa−a−a)×(aaa+aa+a)/((a+a+a)×a).
4019 := (aaa × aaa − (aa + aa) × (aa + a))/((a + a + a) × a).
4020 := (aaa + aaa + aaa + a + a) × (aa + a)/(a × a).
4021 := ((aaa + a) × aaa/(a + a + a) − aaa − aa − a)/a.
4022 := ((aaa + a) × aaa/(a + a + a) − aaa − aa)/a.
4023 := ((aa + aa + aa) × (aaa + aa)/a − a − a − a)/a.
4024 := ((aa + aa + aa) × (aaa + aa)/a − a − a)/a.
4025 := ((aa + aa + aa) × (aaa + aa)/a − a)/a.
4026 := (aa + aa + aa) × (aaa + aa)/(a × a).
4027 := ((aa + aa + aa) × (aaa + aa)/a + a)/a.
4028 := ((aa + aa + aa) × (aaa + aa)/a + a + a)/a.
4029 := ((aa + aa + aa) × (aaa + aa)/a + a + a + a)/a.
4030 := ((aaa − a − a − a) × (aaa + a)/(a + a + a) − a − a)/a.
4031 := ((aaa − a − a − a) × (aaa + a)/(a + a + a) − a)/a.
4032 := (aaa − a − a − a) × (aaa + a)/((a + a + a) × a).
4033 := (aaa − a − a) × aaa/((a + a + a) × a).
4034 := ((aaa − a − a) × aaa/(a + a + a) + a)/a.
4035 := ((aaa − a − a) × aaa/(a + a + a) + a + a)/a.
4036 := ((aaaa − aa + a) × aa/(a + a + a) − a)/a.
4037 := (aaaa − aa + a) × aa/((a + a + a) × a).
34
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4038 := ((aaaa − aa + a) × aa/(a + a + a) + a)/a.
4039 := ((aaaa − aa + a) × aa/(a + a + a) + a + a)/a.
4040 := (aaaaa − a) × (a + a) × (a + a)/(aa × a × a).
4041 := ((aaaaa − a) × (aa − a − a − a)/aa + a + a)/(a + a).
4042 := ((aaaaa − a)/aa × (a + a) + a) × (a + a)/(a × a).
4043 := ((aaa + a) × aaa/(a + a + a) − aaa + aa − a)/a.
4044 := ((aaa + a) × aaa/(a + a + a) − aaa + aa)/a.
4045 := ((aaa + a) × aaa/(a + a + a) − aaa + aa + a)/a.
4046 := ((aaa + a) × aaa/(a + a + a) − aaa + aa + a + a)/a.
4047 := ((aaaa − aa + a + a + a + a) × aa/(a + a + a) − a)/a.
4048 := (aaaa − aa + a + a + a + a) × aa/((a + a + a) × a).
4049 := ((aaa + a) × aaa/(aa + a) + aaaaa)/(a + a + a).
4050 := (aaa/(a + a + a) × aa − a − a) × (aa − a)/(a × a).
4051 := ((aaa + aaa)/(a + a + a) × aaa − aaa − a)/(a + a).
4052 := ((aaa + aaa)/(a + a + a) × aaa − aaa + a)/(a + a).
4053 := ((aaa+a)×aaa/(a+a+a)−aaa+aa+aa−a−a)/a.
4054 := ((aaa + a) × aaa/(a + a + a) − aaa + aa + aa − a)/a.
4055 := ((aaa + a) × aaa/(a + a + a) − aaa + aa + aa)/a.
4056 := ((aa + aa + aa) × (aaa + aa + a)/a − a − a − a)/a.
4057 := ((aa + aa + aa) × (aaa + aa + a)/a − a − a)/a.
4058 := ((aa + aa + aa) × (aaa + aa + a)/a − a)/a.
4059 := (aa + aa + aa) × (aaa + aa + a)/(a × a).
4060 := ((aa + aa + aa) × (aaa + aa + a)/a + a)/a.
4061 := ((aa + aa + aa) × (aaa + aa + a)/a + a + a)/a.
4062 := ((aaaaa − a)/aa × (a + a) + aa) × (a + a)/(a × a).
4063 := (aaa × aaa − (aa + a) × aa)/((a + a + a) × a).
4064 := ((aaa × aaa − (aa + a) × aa)/(a + a + a) + a)/a.
4065 := (aaaa×aa−(aa+a+a)×(a+a))/((a+a+a)×a).
4066 := (aaaaa + aaaa − aa − aa − a − a)/(a + a + a).
4067 := ((aaaa − a)/(a + a + a) × aa − a − a − a)/a.
4068 := ((aaaa − a)/(a + a + a) × aa − a − a)/a.
4069 := ((aaaa − a)/(a + a + a) × aa − a)/a.
4070 := ((aaaa − a)/(a + a + a) × aa)/a.
4071 := ((aaaa − a)/(a + a + a) × aa + a)/a.
4072 := ((aaaa − a)/(a + a + a) × aa + a + a)/a.
4073 := ((aaaa − a)/(a + a + a) × aa + a + a + a)/a.
4074 := (aaaaa + aaaa)/(a + a + a).
4075 := (aaaaa + aaaa + a + a + a)/(a + a + a).
4076 := (aaaaa + aaaa)/(a + a + a) + (a + a)/a.
4077 := (aaaaa + aaaa + aa − a − a)/(a + a + a).
4078 := (aaaaa + aaaa + aa + a)/(a + a + a).
4079 := ((aaaa − a)/(a + a + a) × aa + aa − a − a)/a.
4080 := ((aaaa − a)/(a + a + a) × aa + aa − a)/a.
4081 := (aaaa + a + a) × aa/((a + a + a) × a).
4082 := ((aaaa − a)/(a + a + a) × aa + aa + a)/a.
4083 := ((aaaa − a)/(a + a + a) × aa + aa + a + a)/a.
4084 := (aaa/(a + a + a) × aaa − aa − aa − a)/a.
4085 := (aaa/(a + a + a) × aaa − aa − aa)/a.
4086 := (aaa/(a + a + a) × aaa − aa − aa + a)/a.
4087 := (aaa/(a + a + a) × aaa − aa − aa + a + a)/a.
4088 := ((aaa + aaa − a) × aaa/(a + a + a) − a)/(a + a).
4089 := ((aaa + aaa − a) × aaa/(a + a + a) + a)/(a + a).
4090 := (aaa/(a + a + a) × aa + a + a) × (aa − a)/(a × a).
4091 := ((aaa + aa + a + a) × (aa + aa + aa)/a − a)/a.
4092 := (aaa + aa + a + a) × (aa + aa + aa)/(a × a).
4093 := (aaa/(a + a + a) × aaa − aa − a − a − a)/a.
4094 := (aaa/(a + a + a) × aaa − aa − a − a)/a.
4095 := (aaa/(a + a + a) × aaa − aa − a)/a.
4096 := (aaa/(a + a + a) × aaa − aa)/a.
4097 := (aaa/(a + a + a) × aaa − aa + a)/a.
4098 := (aaa/(a + a + a) × aaa − aa + a + a)/a.
4099 := (aaa/(a + a + a) × aaa − aa + a + a + a)/a.
4100 := (aaa/(a + a + a) × aaa − aa + a + a + a + a)/a.
4101 := (aaa/(a + a + a) × aaa − a − a − a − a − a − a)/a.
4102 := (aaa/(a + a + a) × aaa − a − a − a − a − a)/a.
4103 := (aaa/(a + a + a) × aaa − a − a − a − a)/a.
4104 := (aaa/(a + a + a) × aaa − a − a − a)/a.
4105 := (aaa/(a + a + a) × aaa − a − a)/a.
4106 := (aaa/(a + a + a) × aaa − a)/a.
4107 := (aaa/(a + a + a) × aaa)/a.
4108 := (aaa/(a + a + a) × aaa + a)/a.
4109 := (aaa/(a + a + a) × aaa + a + a)/a.
4110 := (aaa/(a + a + a) × aaa + a + a + a)/a.
4111 := (aaaaa + aaaa + aaa)/(a + a + a).
4112 := ((aaaa + aa) × aa/(a + a + a) − a − a)/a.
4113 := ((aaaa + aa) × aa/(a + a + a) − a)/a.
4114 := (aaaa + aa) × aa/((a + a + a) × a).
4115 := ((aaaa + aa) × aa/(a + a + a) + a)/a.
4116 := (aaa/(a + a + a) × aaa + aa − a − a)/a.
4117 := (aaa/(a + a + a) × aaa + aa − a)/a.
4118 := (aaa/(a + a + a) × aaa + aa)/a.
4119 := (aaa/(a + a + a) × aaa + aa + a)/a.
4120 := (aaa/(a + a + a) × aaa + aa + a + a)/a.
4121 := (aaa/(a + a + a) × aaa + aa + a + a + a)/a.
4122 := (aaa/(a + a + a) × aaa + aa + a + a + a + a)/a.
4123 := (aa + aa + aa − a − a) × (aaa + aa + aa)/(a × a).
4124 := ((aaaa + aa + a + a + a) × aa/(a + a + a) − a)/a.
4125 := (aaaa + aa + a + a + a) × aa/((a + a + a) × a).
4126 := ((aaa + aaa + a) × aaa/(a + a + a) + a)/(a + a).
4127 := ((aaaa + aa + a + a + a) × aa/(a + a + a) + a + a)/a.
4128 := (aaa + aaa + aaa + aa) × (aa + a)/(a × a).
4129 := (aaa/(a + a + a) × aaa + aa + aa)/a.
4130 := (aaa/(a + a + a) × aaa + aa + aa + a)/a.
4131 := ((aaa + a) × aaa/(a + a + a) − aa − a − a)/a.
4132 := ((aaa + a) × aaa/(a + a + a) − aa − a)/a.
4133 := ((aaa + a) × aaa/(a + a + a) − aa)/a.
4134 := ((aaa + a) × aaa/(a + a + a) − aa + a)/a.
4135 := ((aaa + a) × aaa/(a + a + a) − aa + a + a)/a.
4136 := ((aa + aa + aa + a) × (aaa + aa)/a − aa − a)/a.
4137 := ((aa + aa + aa + a) × (aaa + aa)/a − aa)/a.
4148 := ((aa + aa + aa + a) × (aaa + aa)/a − aa + a)/a.
4139 := ((aa + aa + aa + a) × (aaa + aa)/a − aa + a + a)/a.
4140 := (aaa + aaa + aaa + aa + a) × (aa + a)/(a × a).
4141 := (aaa + aa + a) × aaaa/((a + a + a) × aa).
4142 := ((aaa + a) × aaa/(a + a + a) − a − a)/a.
4143 := ((aaa + a) × aaa/(a + a + a) − a)/a.
4144 := (aaa + a) × aaa/((a + a + a) × a).
4145 := ((aaa + a) × aaa/(a + a + a) + a)/a.
4146 := ((aaa + a) × aaa/(a + a + a) + a + a)/a.
4147 := ((aaa + a) × aaa/(a + a + a) + a + a + a)/a.
4148 := (aa + aa + aa + a) × (aaa + aa)/(a × a).
4149 := ((aa + aa + aa + a) × (aaa + aa)/a + a)/a.
4150 := ((aa + aa + aa + a) × (aaa + aa)/a + a + a)/a.
4151 := ((aa + aa + aa + a) × (aaa + aa)/a + a + a + a)/a.
4152 := ((aaa + a) × aaa/(a + a + a) + aa − a − a − a)/a.
4153 := ((aaa + a) × aaa/(a + a + a) + aa − a − a)/a.
4154 := ((aaa + a) × aaa/(a + a + a) + aa − a)/a.
4155 := ((aaa + a) × aaa/(a + a + a) + aa)/a.
4156 := ((aaa + a) × aaa/(a + a + a) + aa + a)/a.
4157 := ((aaa + a) × aaa/(a + a + a) + aa + a + a)/a.
4158 := (aaaa + aa + aa + a) × aa/((a + a + a) × a).
4159 := ((aaaa + aa + aa + a) × aa/(a + a + a) + a)/a.
4160 := (aaa × aaa/(aa − a − a) + aaaaa)/(a + a + a).
4161 := ((aaaa+aa+aa+a)×aa/(a+a+a)+a+a+a)/a.
4162 := ((aaaaa − aa) × (aa − a − a)/(aa + a) − a)/(a + a).
4163 := ((aaaaa − aa) × (aa − a − a)/(aa + a) + a)/(a + a).
4164 := ((aaa + a) × aaa/(a + a + a) + aa + aa − a − a)/a.
4165 := ((aaa + a) × aaa/(a + a + a) + aa + aa − a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4166 := ((aaa + a) × aaa/(a + a + a) + aa + aa)/a.
4167 := (aaaaa + a)/(aa − a − a − a) × (a + a + a)/a.
4168 := ((aaa + a + a) × aaa/(a + a + a) − aa − a − a)/a.
4169 := ((aaa + a + a) × aaa/(a + a + a) − aa − a)/a.
4170 := ((aaa + a + a) × aaa/(a + a + a) − aa)/a.
4171 := ((aaa + a + a) × aaa/(a + a + a) − aa + a)/a.
4172 := ((aaa + a + a) × aaa/(a + a + a) − aa + a + a)/a.
4173 := ((aaa + a + a) × aaa/(a + a + a) − aa + a + a + a)/a.
4174 := ((aaa+a+a)×aaa/(a+a+a)−aa+a+a+a+a)/a.
4175 := ((aaa + aa + a + a) × aaaa/aa + a)/(a + a + a).
4176 := ((aaa+a+a)×aaa/(a+a+a)−a−a−a−a−a)/a.
4177 := ((aaa + a + a) × aaa/(a + a + a) − a − a − a − a)/a.
4178 := ((aaa + aa + a) × aaaa/aa + aaa)/(a + a + a).
4179 := ((aaa + a + a) × aaa/(a + a + a) − a − a)/a.
4180 := ((aaa + a + a) × aaa/(a + a + a) − a)/a.
4181 := (aaa + a + a) × aaa/((a + a + a) × a).
4182 := ((aaa + a + a) × aaa/(a + a + a) + a)/a.
4183 := ((aaa + a + a) × aaa/(a + a + a) + a + a)/a.
4184 := ((aaa + a + a) × aaa/(a + a + a) + a + a + a)/a.
4185 := ((aaa + aaa + aaa − aa) × (aa + a + a)/a − a)/a.
4186 := (aaa + aaa + aaa − aa) × (aa + a + a)/(a × a).
4187 := ((aaa + aaa + aaa − aa) × (aa + a + a)/a + a)/a.
4188 := ((aaa + a) × aaa + (aa + a) × aa)/((a + a + a) × a).
4169 := ((aaa + a + a) × aaa/(a + a + a) + aa − a − a − a)/a.
4190 := ((aaa + a + a) × aaa/(a + a + a) + aa − a − a)/a.
4191 := ((aaa + a + a) × aaa/(a + a + a) + aa − a)/a.
4182 := ((aaa + a + a) × aaa/(a + a + a) + aa)/a.
4193 := ((aaa + a + a) × aaa/(a + a + a) + aa + a)/a.
4194 := (aaa/(a + a + a) × aaa + aaa − aa − aa − a − a)/a.
4195 := (aaa/(a + a + a) × aaa + aaa − aa − aa − a)/a.
4196 := (aaa/(a + a + a) × aaa + aaa − aa − aa)/a.
4197 := (aaa/(a + a + a) × aaa + aaa − aa − aa + a)/a.
4198 := (aaaa + aaaa − aaa − aa − a) × (a + a)/(a × a).
4199 := ((aaaa + aaaa − aaa − aa) × (a + a)/a − a)/a.
4200 := (aaaa + aaaa − aaa − aa) × (a + a)/(a × a).
4201 := ((aaaa + aaaa − aaa − aa) × (a + a)/a + a)/a.
4202 := (aaaa+aa+aa+aa+a+a)×aa/((a+a+a)×a).
4203 := (aaa/(a+a+a)×aaa+aaa−aa−a−a−a−a)/a.
4204 := (aaa/(a + a + a) × aaa + aaa − aa − a − a − a)/a.
4205 := (aaa/(a + a + a) × aaa + aaa − aa − a − a)/a.
4206 := (aaa/(a + a + a) × aaa + aaa − aa − a)/a.
4207 := (aaa/(a + a + a) × aaa + aaa − aa)/a.
4208 := (aaa/(a + a + a) × aaa + aaa − aa + a)/a.
4209 := (aaa/(a + a + a) × aaa + aaa − aa + a + a)/a.
4210 := (aaa/(a + a + a) × aaa + aaa − aa + a + a + a)/a.
4211 := ((aaaa + aaaa − aaa − aa) × (a + a)/a + aa)/a.
4212 := ((aaaa + aaaa − aaa + a) × (a + a)/a − aa − a)/a.
4213 := ((aaaa + aaaa − aaa + a) × (a + a)/a − aa)/a.
4214 := (aaa/(a + a + a) × aaa + aaa − a − a − a − a)/a.
4215 := (aaa/(a + a + a) × aaa + aaa − a − a − a)/a.
4216 := (aaa/(a + a + a) × aaa + aaa − a − a)/a.
4217 := (aaa/(a + a + a) × aaa + aaa − a)/a.
4218 := (aaa/(a + a + a) × aaa + aaa)/a.
4219 := (aaa/(a + a + a) × aaa + aaa + a)/a.
4220 := (aaa/(a + a + a) × aaa + aaa + a + a)/a.
4221 := (aaa/(a + a + a) × aaa + aaa + a + a + a)/a.
4222 := (aaaa + aaaa − aaa) × (a + a)/(a × a).
4223 := ((aaaa + aaaa − aaa) × (a + a)/a + a)/a.
4224 := (aaaa + aaaa − aaa + a) × (a + a)/(a × a).
4225 := ((aaaa + aaaa − aaa + a) × (a + a)/a + a)/a.
4226 := (aaaa + aaaa − aaa + a + a) × (a + a)/(a × a).
4227 := (aaa/(a + a + a) × aaa + aaa + aa − a − a)/a.
4228 := (aaa/(a + a + a) × aaa + aaa + aa − a)/a.
4229 := (aaa/(a + a + a) × aaa + aaa + aa)/a.
35
4230 := (aaa/(a + a + a) × aaa + aaa + aa + a)/a.
4231 := (aaa/(a + a + a) × aaa + aaa + aa + a + a)/a.
4232 := (aaa/(a + a + a) × aaa + aaa + aa + a + a + a)/a.
4233 := ((aaaa + aaaa − aaa + aa) × (a + a)/a − aa)/a.
4234 := ((aaaa + aaaa − aaa + aa) × (a + a)/a − aa + a)/a.
4235 := (aaaa + aa + aa + aa + aa) × aa/((a + a + a) × a).
4236 := ((aaaa + aa + aa + aa + aa) × aa/(a + a + a) + a)/a.
4237 := (aaa/(a+a+a)×aaa+aaa+aa+aa−a−a−a)/a.
4238 := (aaa/(a + a + a) × aaa + aaa + aa + aa − a − a)/a.
4239 := (aaa/(a + a + a) × aaa + aaa + aa + aa − a)/a.
4240 := (aaa/(a + a + a) × aaa + aaa + aa + aa)/a.
4241 := ((aaaa + aaaa) × (aa + aa − a)/aa − a)/a.
4242 := (aa + aa − a) × aaaa × (a + a)/(aa × a × a).
4243 := ((aaaa + aaaa) × (aa + aa − a)/aa + a)/a.
4244 := (aaaa + aaaa − aaa + aa) × (a + a)/(a × a).
4245 := ((aaaa + aaaa − aaa + aa) × (a + a)/a + a)/a.
4246 := (aaaa + aaaa − aaa + aa + a) × (a + a)/(a × a).
4247 := ((aaaa + aaaa − aaa + aa + a) × (a + a)/a + a)/a.
4248 := ((aaaa+aaaa−aaa+aa+a)×(a+a)/a+a+a)/a.
4249 := (aaa/(a+a+a)×aaa+aaa+aa+aa+aa−a−a)/a.
4250 := (aaaaa − aa)/(a + a + a) + (aaaa − aa)/(a + a).
4251 := ((aaa+a)×aaa/(a+a+a)+aaa−a−a−a−a)/a.
4252 := ((aaa + a) × aaa/(a + a + a) + aaa − a − a − a)/a.
4253 := ((aaa + a) × aaa/(a + a + a) + aaa − a − a)/a.
4254 := ((aaa + a) × aaa/(a + a + a) + aaa − a)/a.
4255 := ((aaa + a) × aaa/(a + a + a) + aaa)/a.
4256 := (aaa + a + a + a) × (aaa + a)/((a + a + a) × a).
4257 := ((aaa + a) × aaa/(a + a + a) + aaa + a + a)/a.
4258 := ((aaa + a) × aaa/(a + a + a) + aaa + a + a + a)/a.
4259 := (aaaaa + a)/(a + a + a) + (aaaa − a)/(a + a).
4260 := (aaaaa + a)/(a + a + a) + (aaaa + a)/(a + a).
4261 := (aaaaa − aa)/(a + a + a) + (aaaa + aa)/(a + a).
4262 := ((aaaaa − a)/aa × (a + a) + aaa) × (a + a)/(a × a).
4263 := (aaaa/aa × (a + a) + a) × (aa + aa − a)/(a × a).
4264 := ((aa + aa − a) × aaaa/aa + aa) × (a + a)/(a × a).
4265 := (aaaaa + a)/(a + a + a) + (aaaa + aa)/(a + a).
4266 := ((aaa + a) × aaa/(a + a + a) + aaa + aa)/a.
4267 := ((aaa + a) × aaa/(a + a + a) + aaa + aa + a)/a.
4268 := ((aa + aa + aa + a + a) × (aaa + aa)/a − a − a)/a.
4269 := ((aa + aa + aa + a + a) × (aaa + aa)/a − a)/a.
4270 := (aa + aa + aa + a + a) × (aaa + aa)/(a × a).
4269 := ((aa + aa + aa + a + a) × (aaa + aa)/a + a)/a.
4272 := (aaaaaa/(aa + a + a) × a − a)/(a + a) − a/a.
4273 := (aaaaaa/(aa + a + a) × a − a)/(a + a).
4274 := (aaaaaa/(aa + a + a) × a + a)/(a + a).
4275 := (aaaaaa/(aa + a + a) × a + a)/(a + a) + a/a.
4276 := (aaaaaa/(aa + a + a) × a + a)/(a + a) + (a + a)/a.
4277 := (aaaa + aaa) × (aa + aa − a)/((a + a + a) × (a + a)).
4278 := ((aaa + a + a) × aaa/(a + a + a) + aaa − aa − a −
a − a)/a.
4279 := ((aa+aa+aa+a+a)×(aaa+aa)/a+aa−a−a)/a.
4280 := ((aa + aa + aa + a + a) × (aaa + aa)/a + aa − a)/a.
4281 := ((aa + aa + aa + a + a) × (aaa + aa)/a + aa)/a.
4282 := ((aa + aa + aa + a + a) × (aaa + aa)/a + aa + a)/a.
4283 := ((aaaa + aa) × (aa + aa − a)/aa × (a + a)/a − a)/a.
4284 := (aaaa + aa) × (aa + aa − a)/aa × (a + a)/(a × a).
4285 := ((aaaa + aa) × (aa + aa − a)/aa × (a + a)/a + a)/a.
4286 := ((aaaa−aa)×(aa+a)/(a+a+a)−aaa−a−a−a)/a.
4287 := ((aaaa−aa)×(aa+a)/(a+a+a)−aaa−a−a)/a.
4288 := ((aaaa − aa) × (aa + a)/(a + a + a) − aaa − a)/a.
4289 := ((aaaa − aa) × (aa + a)/(a + a + a) − aaa)/a.
4290 := ((aaa + a + a) × aaa/(a + a + a) + aaa − a − a)/a.
4291 := ((aaa + a + a) × aaa/(a + a + a) + aaa − a)/a.
4292 := ((aaa + a + a) × aaa/(a + a + a) + aaa)/a.
36
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4293 := ((aaa + a + a) × aaa/(a + a + a) + aaa + a)/a.
4294 := (aaa + a + a + a) × (aaa + a + a)/((a + a + a) × a).
4295 := ((aaa + a + a + a) × (aaa + a + a)/(a + a + a) + a)/a.
4296 := ((aaa+a+a+a)×(aaa+a+a)/(a+a+a)+a+a)/a.
4297 := ((aa+aa+aa+aa−a)×(aaa−aa)/a−a−a−a)/a.
4298 := ((aa + aa + aa + aa − a) × (aaa − aa)/a − a − a)/a.
4299 := ((aa + aa + aa + aa − a) × (aaa − aa)/a − a)/a.
4300 := (aa + aa + aa + aa − a) × (aaa − aa)/(a × a).
4301 := ((aa + aa + aa + aa − a) × (aaa − aa)/a + a)/a.
4302 := ((aa + aa + aa + aa − a) × (aaa − aa)/a + a + a)/a.
4303 := (aaa + aaa + aaa − a − a) × (aa + a + a)/(a × a).
4304 := ((aa + aa + aa + a + a) × (aaa + aa + a)/a − a)/a.
4305 := (aa + aa + aa + a + a) × (aaa + aa + a)/(a × a).
4306 := ((aa + aa + aa + a + a) × (aaa + aa + a)/a + a)/a.
4307 := ((aa+aa+aa+a+a)×(aaa+aa+a)/a+a+a)/a.
4308 := (aaaa−aa−aa−aa−a)×(aa+a)/((a+a+a)×a).
4309 := ((aaaa−aa−aa−aa−a)×(aa+a)/(a+a+a)+a)/a.
4310 := ((aaa + aaa + aa) × aaa/(a + a + a) − a)/(a + a).
4311 := ((aaa + aaa + aa) × aaa/(a + a + a) + a)/(a + a).
4312 := ((aaaa + aaaa) × (a + a) − (aa + a) × aa)/(a × a).
4313 := (((aaaa + aaaa) × (a + a) − (aa + a) × aa)/a + a)/a.
4314 := ((aaaa+aaaa+a)×(a+a)−(aa+a)×aa)/(a×a).
4315 := (aaaaa + a)/(a + a + a) + (aaaa + aaa)/(a + a).
4316 := (aaa + aaa + aaa − a) × (aa + a + a)/(a × a).
4317 := ((aaa + aaa + aaa − a) × (aa + a + a)/a + a)/a.
4318 := ((aaa + aaa + aaa − a) × (aa + a + a)/a + a + a)/a.
4319 := ((aaa+aaa+aaa−a)×(aa+a+a)/a+a+a+a)/a.
4320 := (((aaaa + aaaa − a) × (a + a) − aa × aa)/a − a)/a.
4321 := ((aaaa + aaaa − a) × (a + a) − aa × aa)/(a × a).
4322 := (((aaaa + aaaa) × (a + a) − aa × aa)/a − a)/a.
4323 := ((aaaa + aaaa) × (a + a) − aa × aa)/(a × a).
4324 := (((aaaa + aaaa) × (a + a) − aa × aa)/a + a)/a.
4325 := ((aaaa + aaaa + a) × (a + a) − aa × aa)/(a × a).
4326 := ((aaa + aaa + aaa) × (aa + a + a)/a − a − a − a)/a.
4327 := ((aaa + aaa + aaa) × (aa + a + a)/a − a − a)/a.
4328 := ((aaa + aaa + aaa) × (aa + a + a)/a − a)/a.
4329 := (aaa + aaa + aaa) × (aa + a + a)/(a × a).
4330 := ((aaa + aaa + aaa) × (aa + a + a)/a + a)/a.
4331 := ((aaa + aaa + aaa) × (aa + a + a)/a + a + a)/a.
4332 := ((aaa + aaa + aaa) × (aa + a + a)/a + a + a + a)/a.
4333 := ((aaaa + aaaa) × (aa + aa)/aa − aaa)/a.
4334 := (aaaaaa × (aa + a + a)/aaa − aa)/(a + a + a).
4335 := ((aaaa + aaaa) × (aa + aa)/aa − aaa + a + a)/a.
4336 := (((aaaa + aaaa + a) × (a + a) − aa × aa)/a + aa)/a.
4337 := (aaaaaa × (aa + a + a)/aaa − a − a)/(a + a + a).
4338 := (aaaaaa × (aa + a + a)/aaa + a)/(a + a + a).
4339 := ((aaaaa − (aaa + aa) × aaa/(a + a)) − a)/a.
4340 := (aaaaa − (aaa + aa) × aaa/(a + a))/a.
4341 := (aaaaa − (aaa + aa) × aaa/(a + a) + a)/a.
4342 := (aaa + aaa + aaa + a) × (aa + a + a)/(a × a).
4343 := (aa + aa + aa + aa − a) × aaaa/(aa × a).
4344 := ((aa + aa + aa + aa − a) × aaaa/aa + a)/a.
4345 := ((aa + aa + aa + aa − a) × aaaa/aa + a + a)/a.
4346 := ((aa + aa + aa + aa − a) × aaaa/aa + a + a + a)/a.
4347 := ((aaaa−aa−aa−a−a)×(aa+a)/(a+a+a)−a)/a.
4348 := (aaaa−aa−aa−a−a)×(aa+a)/((a+a+a)×a).
4349 := (aaaaa − (aaa + aa) × aaa/(a + a) + aa − a − a)/a.
4350 := (aaaaa − (aaa + aa) × aaa/(a + a) + aa − a)/a.
4351 := (aaaaa − (aaa + aa) × aaa/(a + a) + aa)/a.
4352 := (aaaa − aa − aa − a) × (aa + a)/((a + a + a) × a).
4353 := ((aaaa − aa − aa − a) × (aa + a)/(a + a + a) + a)/a.
4354 := ((aaaa − aa − aa) × (aa + a)/(a + a + a) − a − a)/a.
4355 := ((aaaa − aa − aa) × (aa + a)/(a + a + a) − a)/a.
4356 := (aaaa − aa − aa) × (aa + a)/((a + a + a) × a).
4357 := ((aaaa − aa − aa) × (aa + a)/(a + a + a) + a)/a.
4358 := ((aaaa − aa − aa) × (aa + a)/(a + a + a) + a + a)/a.
4359 := ((aaaa − aa − aa + a) × (aa + a)/(a + a + a) − a)/a.
4360 := (aaaa − aa − aa + a) × (aa + a)/((a + a + a) × a).
4361 := ((aaaa − aa − aa + a) × (aa + a)/(a + a + a) + a)/a.
4362 := ((aaaa−aa−aa+a)×(aa+a)/(a+a+a)+a+a)/a.
4363 := ((aaaa−aa−aa+a+a)×(aa+a)/(a+a+a)−a)/a.
4364 := (aaaa−aa−aa+a+a)×(aa+a)/((a+a+a)×a).
4365 := ((aaaa−aa−aa+a+a)×(aa+a)/(a+a+a)+a)/a.
4366 := ((aaaa − aa − aa + a + a) × (aa + a)/(a + a + a) +
a + a)/a.
4367 := ((aaaa − aa − aa) × (aa + a)/(a + a + a) + aa)/a.
4368 := (aaa+aaa+aa+a)×(aaa+a)/((a+a)×(a+a+a)).
4369 := ((aaaa×(aa+a)−aaa×(a+a))/(a+a+a)−a)/a.
4370 := (aaaa × (aa + a) − aaa × (a + a))/((a + a + a) × a).
4371 := ((aaaa×(aa+a)−aaa×(a+a))/(a+a+a)+a)/a.
4372 := ((aaaaa−aa−a)×(aa+a+a)/aa−a)/(a+a+a).
4373 := ((aaaaa − a) × (aa + a + a)/aa − aa)/(a + a + a).
4374 := ((aaaa+a)×(aa+a)−aaa×(a+a))/((a+a+a)×a).
4375 := (((aaaa + a) × (aa + a) − aaa × (a + a))/(a + a +
a) + a)/a.
4376 := ((aaaaa − a) × (aa + a + a)/aa − a − a)/(a + a + a).
4377 := ((aaaaa − a) × (aa + a + a)/aa + a)/(a + a + a).
4378 := ((aaaa + a + a) × (aa + a) − aaa × (a + a))/((a +
a + a) × a).
4379 := ((aaaa−aaa+aa)×(aa+a+a)/(a+a+a)−a−a)/a.
4380 := ((aaaaa−a)×(aa+a+a)/aa+aa−a)/(a+a+a).
4381 := (aaaa − aaa + aa) × (aa + a + a)/((a + a + a) × a).
4382 := ((aaaa−aaa+aa)×(aa+a+a)/(a+a+a) +a)/a.
4383 := ((aaaa−aaa+aa)×(aa+a+a)/(a+a+a)+a+a)/a.
4384 := (aaaa−aa−a−a−a−a)×(aa+a)/((a+a+a)×a).
4385 := ((aaaa−aa−a−a−a−a)×(aa+a)/(a+a+a)+a)/a.
4386 := (aa + aa + aa + aa − a) × (aaaa + aa)/(aa × a).
4387 := (aaa−a−a−a−a)×(aaa+aa+a)/((a+a+a)×a).
4388 := (aaaa − aa − a − a − a) × (aa + a)/((a + a + a) × a).
4389 := (aaa + aa + aa) × (aa + aa + aa)/(a × a).
4390 := (aaaaa − (aaaa + aaa)/(a + a) × aa)/a.
4391 := (aaaaa − (aaaa + aaa)/(a + a) × aa + a)/a.
4392 := (aaaa − aa − a − a) × (aa + a)/((a + a + a) × a).
4393 := ((aaaa − aa − a − a) × (aa + a)/(a + a + a) + a)/a.
4394 := (aaaaa − (aa + aa + a) × aaaa/aa)/(a + a).
4397 := ((aaaa − aa − a) × (aa + a)/(a + a + a) − a)/a.
4396 := (aaaa − aa − a) × (aa + a)/((a + a + a) × a).
4397 := ((aaaa − aa − a) × (aa + a)/(a + a + a) + a)/a.
4398 := ((aaaa − aa) × (aa + a)/(a + a + a) − a − a)/a.
4399 := ((aaaa − aa) × (aa + a)/(a + a + a) − a)/a.
4400 := (aaaa − aa) × (aa + a)/((a + a + a) × a).
4401 := ((aaa + aa)/(a + a) × (a − aaa) + aaaaa)/a.
4402 := (aaaa + aaaa − aa − aa + a) × (a + a)/(a × a).
4403 := ((aaa + aa) × aaa/(a + a + a) − aaa)/a.
4404 := (aaaa − aa + a) × (aa + a)/((a + a + a) × a).
4405 := ((aaa + aa) × aaa/(a + a + a) − aaa + a + a)/a.
4406 := ((aaa + aa) × aaa/(a + a + a) − aaa + a + a + a)/a.
4407 := ((aaaa − aa + a + a) × (aa + a)/(a + a + a) − a)/a.
4408 := (aaaa − aa + a + a) × (aa + a)/((a + a + a) × a).
4409 := ((aaaa + aaaa − aa) × (a + a)/a − aa − a − a)/a.
4410 := ((aaaa + aaaa − aa) × (a + a)/a − aa − a)/a.
4411 := ((aaaa + aaaa − aa) × (a + a)/a − aa)/a.
4412 := ((aaaa + aaaa − aa) × (a + a)/a − aa + a)/a.
4413 := ((aaaa + aaaa − aa) × (a + a)/a − aa + a + a)/a.
4414 := ((aaaa+aaaa−aa−a−a−a)×(a+a)/a−a−a)/a.
4415 := ((aaaa + aaaa − aa − a − a − a) × (a + a)/a − a)/a.
4416 := (aaaa + aaaa − aa − a − a − a) × (a + a)/(a × a).
4417 := ((aaaa + aaaa − aa − a − a) × (a + a)/a − a)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4418 := (aaaa + aaaa − aa − a − a) × (a + a)/(a × a).
4419 := ((aaaa + aaaa − aa − a − a) × (a + a)/a + a)/a.
4420 := (aaaa + aaaa − aa − a) × (a + a)/(a × a).
4421 := ((aaaa + aaaa − aa) × (aa + aa)/aa − a)/a.
4422 := (aaaa + aaaa − aa) × (a + a)/(a × a).
4423 := ((aaaa + aaaa − aa) × (aa + aa)/aa + a)/a.
4424 := (aaaa + aaaa − aa + a) × (a + a)/(a × a).
4425 := ((aaaa + aaaa − aa + a) × (a + a)/a + a)/a.
4426 := (aaaa + aaaa − aa + a + a) × (a + a)/(a × a).
4427 := ((aaaa + aaaa − aa + a) × (a + a)/a + a)/a.
4428 := (aaaa − a − a − a − a) × (aa + a)/((a + a + a) × a).
4429 := ((aaaa − a − a − a − a) × (aa + a)/(a + a + a) + a)/a.
4430 := (aaa + aaa + aaa + aaa − a) × (aa − a)/(a × a).
4431 := ((aaaa + aaaa − a) × (aa + aa)/aa − aa)/a.
4432 := (aaaa × (aa + a)/(a + a + a) − aa − a)/a.
4433 := (aaaa × (aa + a)/(a + a + a) − aa)/a.
4434 := (aaaa × (aa + a)/(a + a + a) − aa + a)/a.
4435 := (aaaa × (aa + a)/(a + a + a) − aa + a + a)/a.
4436 := (aaaa − a − a) × (aa + a)/((a + a + a) × a).
4437 := ((aaaa − a − a) × (aa + a)/(a + a + a) + a)/a.
4438 := (aaaa + aaaa − a − a − a) × (a + a)/(a × a).
4439 := (aaaaa − aaaa − aaaa − aa)/(a + a).
4440 := (aaaa + aaaa − a − a) × (a + a)/(a × a).
4441 := ((aaaa + aaaa − a) × (a + a)/a − a)/a.
4442 := (aaaa + aaaa − a) × (a + a)/(a × a).
4443 := (aaaa × (aa + a)/(a + a + a) − a)/a.
4444 := aaaa × (aa + a)/((a + a + a) × a).
4445 := (aaaa × (aa + a)/(a + a + a) + a)/a.
4446 := (aaaa + aaaa + a) × (a + a)/(a × a).
4447 := ((aaaa + aaaa + a) × (a + a)/a + a)/a.
4448 := (aaaa + a) × (aa + a)/(a + a + a)/a.
4449 := ((aaaa + a) × (aa + a)/(a + a + a) + a)/a.
4450 := (aaaaa − aaaa − aaaa + aa)/(a + a).
4451 := ((aaaa + a + a) × (aa + a)/(a + a + a) − a)/a.
4452 := (aaaa + a + a) × (aa + a)/((a + a + a) × a).
4453 := ((aaaa + aaaa − a) × (aa + aa)/aa + aa)/a.
4454 := ((aaaa + aaaa) × (aa + aa)/aa + aa − a)/a.
4455 := ((aaaa + aaaa) × (aa + aa)/aa + aa)/a.
4456 := (aaaa + a + a + a) × (aa + a)/((a + a + a) × a).
4457 := ((aaaa + aaaa + a) × (aa + aa)/aa + aa)/a.
4458 := ((aaaa + aaaa + a) × (aa + aa)/aa + aa + a)/a.
4459 := ((aaa + aaa + a) × (aa + aa − a − a)/a − a)/a.
4460 := (aaa + aaa + a) × (aa + aa − a − a)/(a × a).
4461 := ((aaa + aaa + a) × (aa + aa − a − a)/a + a)/a.
4462 := (aaaa + aaaa + aa − a − a) × (a + a)/(a × a).
4463 := ((aaaa + aaaa + aa − a) × (a + a)/a − a)/a.
4464 := (aaaa + aaaa + aa − a) × (a + a)/(a × a).
4465 := ((aaaa + aaaa + aa) × (aa + aa)/aa − a)/a.
4466 := (aaaa + aaaa + aa) × (a + a)/(a × a).
4467 := ((aaaa + aaaa + aa) × (aa + aa)/aa + a)/a.
4468 := (aaaa + aaaa + aa + a) × (a + a)/(a × a).
4469 := (aaa + aa + a) × (aaa − a − a)/((a + a + a) × a).
4470 := (aaaa + aaaa + aa + a + a) × (a + a)/(a × a).
4471 := ((aaa + aaa + aaa + aa) × (aa + a + a)/a − a)/a.
4472 := (aaa + aaa + aaa + aa) × (aa + a + a)/(a × a).
4473 := ((aaa + aaa + aaa + aa) × (aa + a + a)/a + a)/a.
4474 := ((aaa + aa + aa) × aaaa/aa − aa)/(a + a + a).
4475 := ((aaa/(a + a + a) × aa × aa)/a − a − a)/a.
4476 := ((aaa/(a + a + a) × aa × aa)/a − a)/a.
4477 := (aaa/(a + a + a) × aa × aa)/(a × a).
4478 := ((aaa/(a + a + a) × aa × aa)/a + a)/a.
4479 := ((aaa/(a + a + a) × aa × aa)/a + a + a)/a.
4480 := ((aaa/(a + a + a) × aa × aa)/a + a + a + a)/a.
4481 := ((aaa/(a + a + a) × aa × aa)/a + a + a + a + a)/a.
37
4482 := ((aaaa + aa − a) × (aa + a)/(a + a + a) − a − a)/a.
4483 := ((aaaa + aa − a) × (aa + a)/(a + a + a) − a)/a.
4484 := (aaaa + aa − a) × (aa + a)/((a + a + a) × a).
4485 := ((aaaa + aa − a) × (aa + a)/(a + a + a) + a)/a.
4486 := (aaaa + aaaa + aa + aa − a) × (a + a)/(a × a).
4487 := ((aaaa + aa) × (aa + a)/(a + a + a) − a)/a.
4488 := (aaaa + aa) × (aa + a)/((a + a + a) × a).
4489 := ((aaaa + aa) × (aa + a)/(a + a + a) + a)/a.
4490 := (aaaa + aaaa + aa + aa + a) × (a + a)/(a × a).
4491 := ((aaaa + aa + a) × (aa + a)/(a + a + a) − a)/a.
4492 := (aaaa + aa + a) × (aa + a)/((a + a + a) × a).
4493 := ((aaa × aaa − aaaa × (a + a + a))/(a + a) − a)/a.
4494 := (aaa × aaa − aaaa × (a + a + a))/((a + a) × a).
4495 := ((aaa × aaa − aaaa × (a + a + a))/(a + a) + a)/a.
4496 := (aaaa + aa + a + a) × (aa + a)/((a + a + a) × a).
4497 := ((aaaa + aa + a + a) × (aa + a)/(a + a + a) + a)/a.
4498 := ((aaaa − aaa) × (aa − a − a)/(a + a) − a − a)/a.
4499 := ((aaaa − aaa) × (aa − a − a)/(a + a) − a)/a.
4500 := (aaaa − aaa) × (aa − a − a)/(a + a)/a.
4501 := ((aaa − aaaa) × (a − aa + a)/(a + a) + a)/a.
4502 := ((aaa + aa) × aaa/(a + a + a) − aa − a)/a.
4503 := ((aaa + aa) × aaa/(a + a + a) − aa)/a.
4504 := ((aaa + aa) × aaa/(a + a + a) − aa + a)/a.
4505 := ((aaa + aa) × aaa/(a + a + a) − aa + a + a)/a.
4506 := ((aaa + aa) × aaa/(a + a + a) − aa + a + a + a)/a.
4507 := ((aaa−aa)×(aa+a)+aaa×aaa)/((a+a+a)×a).
4508 := (aaa + aaa + aaa − aa) × (aa + a + a + a)/(a × a).
4509 := (aaaaaa + aaa) × (aa − a − a)/aaa/(a + a).
4510 := (aaa + aa + a) × (aaa − a)/((a + a + a) × a).
4511 := ((aaa + aa + a) × (aaa − a)/(a + a + a) + a)/a.
4512 := ((aaa + aa) × aaa/(a + a + a) − a − a)/a.
4513 := ((aaa + aa) × aaa/(a + a + a) − a)/a.
4514 := (aaa + aa) × aaa/((a + a + a) × a).
4515 := ((aaa + aa) × aaa/(a + a + a) + a)/a.
4516 := ((aaa + aa) × aaa/(a + a + a) + a + a)/a.
4517 := ((aaa + aa) × aaa/(a + a + a) + a + a + a)/a.
4518 := ((aaaa − aa − a) × (a + a + a) + aaa × aa)/(a × a).
4519 := ((aaaa + aaa + aa) × aa/(a + a + a) − a − a)/a.
4520 := ((aaaa + aaa + aa) × aa/(a + a + a) − a)/a.
4521 := (aaaa + aaa + aa) × aa/((a + a + a) × a).
4522 := (aa + aa + aa + a) × (aaa + aa + aa)/(a × a).
4523 := ((aa + aa + aa + a) × (aaa + aa + aa)/a + a)/a.
4524 := ((aaa + aa) × aaa/(a + a + a) + aa − a)/a.
4525 := ((aaa + aa) × aaa/(a + a + a) + aa)/a.
4526 := ((aaa + aa) × aaa/(a + a + a) + aa + a)/a.
4527 := ((aaa + aa) × aaa/(a + a + a) + aa + a + a)/a.
4528 := (aaaa + aa + aa − a) × (aa + a)/((a + a + a) × a).
4529 := ((aaaa + aa + aa − a) × (aa + a)/(a + a + a) + a)/a.
4530 := ((aaaa + aa + aa) × (aa + a)/(a + a + a) − a − a)/a.
4531 := ((aaaa + aa + aa) × (aa + a)/(a + a + a) − a)/a.
4532 := (aaaa + aa + aa) × (aa + a)/((a + a + a) × a).
4533 := ((aaaa + aa + aa) × (aa + a)/(a + a + a) + a)/a.
4534 := ((aaaaa − a) × (aa − a − a)/aa − aa − aa)/(a + a).
4535 := ((aaaaa − aa − a) × (aa − a − a)/aa − aa)/(a + a).
4536 := ((aaa + aa) × aaa/(a + a + a) + aa + aa)/a.
4537 := ((aaa + aa) × aaa/(a + a + a) + aa + aa + a)/a.
4538 := ((aaa + a + a) × (aaa − aa)/(a + a) − aaaa − a)/a.
4539 := ((aaa + a + a) × (aaa − aa)/(a + a) − aaaa)/a.
4540 := ((aaa + aa + a)/(a + a + a) × aaa − aa)/a.
4541 := ((aaaaa − aa) × (aa − a − a)/(a + a) + a)/aa.
4542 := ((aaaaa − aa) × (aa − a − a)/(a + a) + aa + a)/aa.
4543 := (aaaa × (a + a + a) + (aaa − a) × aa)/(a × a).
4544 := ((aaaaa − a) × (aa − a − a)/aa − a − a)/(a + a).
4545 := (aaaaa − a) × (aa − a − a)/(aa × (a + a)).
38
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4546 := ((aaaaa − a) × (aa − a − a)/(aa + aa) + a)/a.
4547 := (aaaaaa + aa)/aa − (aaaaa − a)/(a + a).
4548 := ((aaa + aa) × aaa/(a + a + a) + aa + aa + aa + a)/a.
4549 := (aaaaa − aa)/(a + a) − aaaaaa/aaa.
4550 := (aaaa − aaa + a) × (aaa − aa)/((a + a) × aa).
4551 := ((aaa + aa + a)/(a + a + a) × aaa)/a.
4552 := ((aaa + aa + a)/(a + a + a) × aaa + a)/a.
4553 := ((aaa + aa + a)/(a + a + a) × aaa + a + a)/a.
4554 := (aaaa × (a + a + a) + aaa × aa)/(a × a).
4555 := ((aaaa × (a + a + a) + aaa × aa)/a + a)/a.
4556 := ((aaaa × (a + a + a) + aaa × aa)/a + a + a)/a.
4557 := ((aaaa + a) × (a + a + a) + aaa × aa)/(a × a).
4558 := ((aaaa + a) × (aa + a)/(a + a + a) + aaa − a)/a.
4559 := ((aaaa + a) × (aa + a)/(a + a + a) + aaa)/a.
4560 := ((aaaa + a) × (aa + a)/(a + a + a) + aaa + a)/a.
4561 := ((aaa + aa + a)/(a + a + a) × aaa + aa − a)/a.
4562 := ((aaa + aa + a)/(a + a + a) × aaa + aa)/a.
4563 := ((aaaa − a) × aaa/(aa − a − a) − a)/(a + a + a).
4564 := ((aaaa − a) × aaa/(aa − a − a) + a + a)/(a + a + a).
4565 := (aaaa × (a + a + a) + (aaa + a) × aa)/(a × a).
4566 := (aaaa × aaa/(a + a + a) − aa − a − a)/(aa − a − a).
4567 := ((aaaa + aaaa + a) × (a + a) + aa × aa)/(a × a).
4568 := (((aaaa + aaaa + a) × (a + a) + aa × aa)/a + a)/a.
4569 := ((aaaa + aaaa + a + a) × (a + a) + aa × aa)/(a × a).
4570 := (((aaaa+aaaa+a+a)×(a+a)+aa×aa)/a+a)/a.
4571 := ((aaaa+aa+aa+aa−a)×(aa+a)/(a+a+a)−a)/a.
4572 := (aaaa+aa+aa+aa−a)×(aa+a)/((a+a+a)×a).
4573 := (((aa+aa−a)×(aaa+a)+aaaa×(a+a))/a−a)/a.
4574 := ((aa + aa − a) × (aaa + a) + aaaa × (a + a))/(a × a).
4575 := ((aaaaa + a) × (aa − a)/(aa + a) − aaa + a)/(a + a).
4576 := ((aaaa + aaaa) × (a + a) + (aa + a) × aa)/(a × a).
4577 := ((aaa + aa + a + a) × aaa/(a + a + a) − aa)/a.
4578 := ((aaa + aa + a + a) × aaa/(a + a + a) − aa + a)/a.
4579 := ((aaa+aa+a+a)×aaa/(a+a+a)−aa+a+a)/a.
4580 := (aaaa+aa+aa+aa+a)×(aa+a)/((a+a+a)×a).
4581 := ((aaa + aa + a) × (aaa + a)/(a + a + a) − aa)/a.
4592 := ((aaa + aa + a) × (aaa + a)/(a + a + a) + a − aa)/a.
4583 := ((aaa − aaaaa + a) × (a − aa)/(a + a) + a)/(aa + a).
4584 := ((aaaa + aa − a) × (a + a + a) + aaa × aa)/(a × a).
4585 := ((aaa/(a + a + a) × aa + aa − a) × aa/a − a − a)/a.
4586 := ((aaa/(a + a + a) × aa + aa − a) × aa/a − a)/a.
4587 := (aaa/(a + a + a) × aa + aa − a) × aa/(a × a).
4588 := (aaa + aa + a + a) × aaa/((a + a + a) × a).
4589 := ((aaa + aa + a + a) × aaa/(a + a + a) + a)/a.
4590 := ((aaa + aa + a + a) × aaa/(a + a + a) + a + a)/a.
4591 := ((aaa + aa + a) × (aaa + a)/(a + a + a) − a)/a.
4592 := (aaa + aa + a) × (aaa + a)/((a + a + a) × a).
4593 := ((aaa + aa + a) × (aaa + a)/(a + a + a) + a)/a.
4594 := ((aaa + aa + a) × (aaa + a)/(a + a + a) + a + a)/a.
4595 := ((aaa/(a + a + a) × aa + aa) × aa/a − a − a − a)/a.
4596 := ((aaa/(a + a + a) × aa + aa) × aa/a − a − a)/a.
4597 := ((aaa/(a + a + a) × aa + aa) × aa/a − a)/a.
4598 := (aaa/(a + a + a) × aa + aa) × aa/(a × a).
4599 := ((aaa/(a + a + a) × aa + aa) × aa/a + a)/a.
4600 := (aaa + aaa − aa − aa) × (aa + aa + a)/(a × a).
4601 := ((a − aaaaa) × (a − aa + a)/aa + aaa + a)/(a + a).
4602 := ((aaa + aaa − aa − aa) × (aa + aa + a)/a + a + a)/a.
4603 := ((aaa + aa) × aaa/(a + a + a) + aaa − aa − aa)/a.
4604 := ((aaa+aa)×aaa/(a+a+a)+aaa−aa−aa+a)/a.
4605 := ((aaa × aaa − aaaa × (a + a + a))/(a + a) + aaa)/a.
4606 := ((aaa+aaa−aa−a)×(aa+aa)/a−aa−a−a−a)/a.
4607 := ((aaa + aaa − aa − a) × (aa + aa)/a − aa − a − a)/a.
4608 := ((aaa + aaa − aa − a) × (aa + aa)/a − aa − a)/a.
4609 := ((aaa + aaa − aa − a) × (aa + aa)/a − aa)/a.
4610 := ((aaa + aaa − aa − a) × (aa + aa)/a − aa + a)/a.
4611 := ((aaa + aaa − aa − a) × (aa + aa)/a − aa + a + a)/a.
4612 := ((aaaa+aa)×aaa/(aa−a−a)−a−a)/(a+a+a).
4613 := ((aaaa + aa) × aaa/(aa − a − a) + a)/(a + a + a).
4614 := ((aaa + aa) × aaa/(a + a + a) + aaa − aa)/a.
4615 := ((aaa + aa) × aaa/(a + a + a) + aaa − aa + a)/a.
4616 := ((aaa + aa) × aaa/(a + a + a) + aaa − aa + a + a)/a.
4617 := ((aaa + aaa − aa − a) × (aa + aa)/a − a − a − a)/a.
4618 := ((aaa + aaa − aa − a) × (aa + aa)/a − a − a)/a.
4619 := ((aaa + aaa − aa − a) × (aa + aa)/a − a)/a.
4620 := (aaa + aaa − aa − a) × (aa + aa)/(a × a).
4621 := ((aaa + aaa − aa − a) × (aa + aa)/a + a)/a.
4622 := ((aaa + aaa − aa − a) × (aa + aa)/a + a + a)/a.
4623 := (aaaa + aaaa − aa) × (aa + aa + a)/(aa × a).
4624 := ((aaa + aa) × aaa/(a + a + a) + aaa − a)/a.
4625 := ((aaa + aa) × aaa/(a + a + a) + aaa)/a.
4626 := ((aaa + aa) × aaa/(a + a + a) + aaa + a)/a.
4627 := ((aaa + aa) × aaa/(a + a + a) + aaa + a + a)/a.
4628 := ((aaa + aa) × aaa/(a + a + a) + aaa + a + a + a)/a.
4629 := (aaaaa − a)/(a + a) − (aaaaa + a)/(aa + a).
4630 := (aaaaa + a) × (aa − a)/((aa + a) × (a + a)).
4631 := ((aaaaa + a) × (aa − a)/(aa + a) + a + a)/(a + a).
4632 := ((aaa + aa + a) × (aaa + a + a)/(a + a + a) − a)/a.
4633 := (aaa + aa + a) × (aaa + a + a)/((a + a + a) × a).
4634 := ((aaa + aa + a) × (aaa + a + a)/(a + a + a) + a)/a.
4635 := ((aaaaa + a) × (aa − a)/(aa + a) + aa − a)/(a + a).
4636 := (aaa + a + a + a) × (aaa + aa)/((a + a + a) × a).
4637 := ((aaaa + a + a) × (aaa − aa)/(aa + a) − a)/(a + a).
4638 := ((aaaa + a + a) × (aaa − aa)/(aa + a) + a)/(a + a).
4639 := ((aaa + aaa − a) × (aa + aa − a)/a − a − a)/a.
4640 := ((aaa + aaa − a) × (aa + aa − a)/a − a)/a.
4641 := (aaa + aaa − a) × (aa + aa − a)/(a × a).
4642 := (aaa + aaa − aa) × (aa + aa)/(a × a).
4643 := ((aaa + aaa − aa) × (aa + aa)/a + a)/a.
4644 := ((aaa + aaa − aa) × (aa + aa)/a + a + a)/a.
4645 := ((aa + aa + a) × aaaa/aa × (a + a)/a − a)/a.
4646 := (aa + aa + a) × aaaa/aa × (a + a)/(a × a).
4647 := ((aaaa + aaaa) × (aa + aa + a)/aa + a)/a.
4648 := ((aa + aa + a) × aaaa/aa + a) × (a + a)/(a × a).
4649 := ((aaa + aaa) × (aa + aa − a)/a − aa − a − a)/a.
4650 := ((aaa + aaa) × (aa + aa − a)/a − aa − a)/a.
4651 := ((aaa + aaa) × (aa + aa − a)/a − aa)/a.
4652 := ((aaa + aaa) × (aa + aa − a)/a − aa + a)/a.
4653 := ((aaa + aaa) × (aa + aa − a)/a − aa + a + a)/a.
4654 := ((aaaa + aaaa + aaa) × (a + a)/a − aa − a)/a.
4655 := ((aaaa + aaaa + aaa) × (a + a)/a − aa)/a.
4655 := ((aaaa + aaaa + aaa) × (a + a)/a − aa + a)/a.
4657 := ((aaaa + aaaa) × (aa + aa + a)/aa + aa)/a.
4658 := ((aaa + aaa) × (aa + aa − a)/a − a − a − a − a)/a.
4659 := ((aaa + aaa) × (aa + aa − a)/a − a − a − a)/a.
4660 := ((aaa + aaa) × (aa + aa − a)/a − a − a)/a.
4661 := ((aaa + aaa) × (aa + aa − a)/a − a)/a.
4662 := (aaa + aaa) × (aa + aa − a)/(a × a).
4663 := ((aaa + aaa) × (aa + aa − a)/a + a)/a.
4664 := ((aaa + aaa) × (aa + aa − a)/a + a + a)/a.
4665 := ((aaaa + aaaa + aaa) × (a + a)/a − a)/a.
4666 := (aaaa + aaaa + aaa) × (a + a)/(a × a).
4667 := ((aaaa + aaaa + aaa) × (a + a)/a + a)/a.
4668 := (aaaa + aaaa + aaa + a) × (a + a)/(a × a).
4669 := (aaaa + aaaa + aa) × (aa + aa + a)/(aa × a).
4670 := (aaaa + aaaa + aaa + a + a) × (a + a)/(a × a).
4671 := ((aaa + aaa) × (aa + aa − a)/a + aa − a − a)/a.
4672 := ((aaa + aaa) × (aa + aa − a)/a + aa − a)/a.
4673 := ((aaa + aaa) × (aa + aa − a)/a + aa)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4674 := ((aaa + aaa) × (aa + aa − a)/a + aa + a)/a.
4675 := (aaaa + aa) × (aaa − aa)/(aa + a)/(a + a).
4676 := ((aaa + aaa) × (aa + aa − a)/a + aa + a + a + a)/a.
4677 := ((aaaa + aaaa + aaa) × (a + a)/a + aa)/a.
4678 := ((aaaa + aaaa + aaa) × (a + a)/a + aa + a)/a.
4679 := ((aaa + aaa + aa + a) × (aa + aa − a − a)/a − a)/a.
4680 := (aaa + aaa + aa + a) × (aa + aa − a − a)/(a × a).
4681 := ((aaa + aaa + a) × (aa + aa − a)/a − a − a)/a.
4682 := ((aaa + aaa + a) × (aa + aa − a)/a − a)/a.
4683 := (aaa + aaa + a) × (aa + aa − a)/(a × a).
4684 := ((aaa + aaa + a) × (aa + aa − a)/a + a)/a.
4685 := ((aaa + aaa + a) × (aa + aa − a)/a + a + a)/a.
4686 := ((aaa + aaa + a) × (aa + aa − a)/a + a + a + a)/a.
4687 := ((aaaa + aaaa + aaa + aa) × (a + a)/a − a)/a.
4688 := (aaaa + aaaa + aaa + aa) × (a + a)/(a × a).
4689 := ((aaaa + aaaa + aaa + aa) × (a + a)/a + a)/a.
4690 := (aaaa + aaaa + aaa + aa + a) × (a + a)/(a × a).
4691 := ((aaa + aaa + aa + a) × (aa + aa − a − a)/a + aa)/a.
4692 := (aaaa + aa) × (aa + aa + a) × (a + a)/(aa × a × a).
4693 := ((aaa + aaa + a) × (aa + aa − a)/a + aa − a)/a.
4694 := ((aaa + aaa + a) × (aa + aa − a)/a + aa)/a.
4695 := ((aaa + aaa + a) × (aa + aa − a)/a + aa + a)/a.
4696 := ((aaaaa − aa) × aa/(a + a) − a − a)/(aa + a + a).
4697 := ((aaaaa − aa) × aa/(a + a) + aa)/(aa + a + a).
4698 := ((aaaa + aaaa + aaa + aa) × (a + a)/a + aa − a)/a.
4699 := ((aaaa + aaaa + aaa + aa) × (a + a)/a + aa)/a.
4700 := (aaaa + aaa) × (aaa − aa)/((aa + a + a) × (a + a)).
4701 := ((aaa+aaa+a+a)×(aa+aa−a)/a−a−a−a)/a.
4702 := ((aaaaa + a)/(a + a) × aa + aa − a)/(aa + a + a).
4703 := ((aaa + aaa + a + a) × (aa + aa − a)/a − a)/a.
4704 := (aaa + aaa + a + a) × (aa + aa − a)/(a × a).
4705 := (aaaaa + a)/(a + a + a) + aaaaaa/aaa.
4706 := ((aaa + aaa + a + a) × (aa + aa − a)/a + a + a)/a.
4707 := ((aaa+aaa+a+a)×(aa+aa−a)/a+a+a+a)/a.
4708 := ((aaaa+a+a)×(aaa−a)/(a+a)−aa)/(aa+a+a).
4709 := ((aaaaa − a) × aa/(a + a) + aaa + a)/(aa + a + a).
4710 := (aaaaa − aa)/(a + a + a) + (aaaaa − a)/aa.
4711 := ((aaa+aa+a+a)×(aaa+a+a+a)/(a+a+a)−a)/a.
4712 := (aaa+aa+a+a)×(aaa+a+a+a)/((a+a+a)×a).
4713 := ((aaaaa − a) × (aa + a + a + a)/aa − a)/(a + a + a).
4714 := (aaaaa + a)/(a + a + a) + (aaaaa − a)/aa.
4715 := (aaa+a+a+a+a)×(aaa+aa+a)/((a+a+a)×a).
4716 := ((aaa+a+a+a+a)×(aaa+aa+a)/(a+a+a)+a)/a.
4717 := ((aaaa−aa−aa)×(aa+a+a)/(a+a+a)−a−a)/a.
4718 := (aaaa − aaa + aa) × (aaa + a)/((aa + a) × (a + a)).
4719 := (aaaa − aa − aa) × (aa + a + a)/((a + a + a) × a).
4720 := ((aaaa − aa − aa) × (aa + a + a)/(a + a + a) + a)/a.
4721 := ((aaaa−aa−aa)×(aa+a+a)/(a+a+a)+a+a)/a.
4722 := ((aa+aa+aa+a)×aaaa/(a+a)+a)/(a+a+a+a).
4723 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa − aa −
a − a)/a.
4724 := ((aaa+aa)×aaa/(a+a+a)+aaa+aaa−aa−a)/a.
4725 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa − aa)/a.
4726 := (aaaa + aa) × (aaaa + a)/((aa + aa) × (aa + a)).
4727 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa − aa +
a + a)/a.
4728 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa − a −
a − a)/a.
4729 := ((aaa+aaa−aa−a)×(aa+aa)/a+aaa−a−a)/a.
4730 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa − a)/a.
4731 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa)/a.
4732 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa + a)/a.
4733 := ((aaa+aaa−aa−a)×(aa+aa)/a+aaa+a+a)/a.
4734 := ((aaa+aa)×aaa/(a+a+a)+aaa+aaa−a−a)/a.
39
4735 := aaaaaa/(aa + aa − a) − (aaaa + a)/(a + a).
4736 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa)/a.
4737 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa + a)/a.
4738 := ((aaaa − a) × aaa/(a + a) − aa)/(aa + a + a).
4739 := ((aaaa − a) × aaa/(a + a) + a + a)/(aa + a + a).
4740 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa + aa −
a − a)/a.
4741 := ((aaa+aaa−aa−a)×(aa+aa)/a+aaa+aa−a)/a.
4742 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa + aa)/a.
4743 := ((aaa+aaa−aa−a)×(aa+aa)/a+aaa+aa+a)/a.
4744 := ((aaa + aaa − aa − a) × (aa + aa)/a + aaa + aa +
a + a)/a.
4745 := ((aaa + aa + a + a + a + a) × (aaa + a + a)/(a +
a + a) − a)/a.
4746 := (aaa + aa + a + a + a + a) × (aaa + a + a)/((a +
a + a) × a).
4747 := ((aaaa + aa) × (aaa − a)/(a + a) + a)/(aa + a + a).
4748 := ((aaa+aa)×aaa/(a+a+a)+aaa+aaa+aa+a)/a.
4749 := ((aaa + aa) × aaa/(a + a + a) + aaa + aaa + aa +
a + a)/a.
4750 := (aaaa−aaa)×(aaa+a+a+a)/((aa+a)×(a+a)).
4751 := (((aaa + aaa) × (aa + aa) − aa × aa)/a − aa − a)/a.
4752 := (((aaa + aaa) × (aa + aa) − aa × aa)/a − aa)/a.
4753 := (((aaa + aaa) × (aa + aa) − aa × aa)/a − aa + a)/a.
4754 := (((aaa+aaa)×(aa+aa)−aa×aa)/a−aa+a+a)/a.
4755 := ((aaaa − aa − a − a) × (aa + a + a)/(a + a + a) −
a − a − a)/a.
4756 := ((aaaa + a) × aaa/(a + a) + aaa + a)/(aa + a + a).
4757 := ((aaaa−aa−a−a)×(aa+a+a)/(a+a+a)−a)/a.
4758 := (aaaa − aa − a − a) × (aa + a + a)/((a + a + a) × a).
4759 := ((aaaa−aa−a−a)×(aa+a+a)/(a+a+a)+a)/a.
4760 := ((aaaa−aa−a−a)×(aa+a+a)/(a+a+a)+a+a)/a.
4761 := (((aaa + aaa) × (aa + aa) − aa × aa)/a − a − a)/a.
4762 := (((aaa + aaa) × (aa + aa) − aa × aa)/a − a)/a.
4763 := ((aaa + aaa) × (aa + aa) − aa × aa)/(a × a).
4764 := (((aaa + aaa) × (aa + aa) − aa × aa)/a + a)/a.
4765 := (((aaa + aaa) × (aa + aa) − aa × aa)/a + a + a)/a.
4766 := (((aaa+aaa)×(aa+aa)−aa×aa)/a+a+a+a)/a.
4767 := (aaaaa+aa+a)×(aa+a)/((a+a)×(aa+a+a+a)).
4768 := ((aaaa−aa+a)×(aa+a+a)/(a+a+a)−a−a−a)/a.
4769 := ((aaaa−aa+a)×(aa+a+a)/(a+a+a)−a−a)/a.
4770 := ((aaaa − aa + a) × (aa + a + a)/(a + a + a) − a)/a.
4771 := (aaaa − aa + a) × (aa + a + a)/((a + a + a) × a).
4772 := ((aaaa − aa + a) × (aa + a + a)/(a + a + a) + a)/a.
4773 := (aaaaaa/aa − (aaaa − a)/(a + a)) × a/(a + a).
4774 := (aaaa × (aa + a + a) − aa × aa)/((a + a + a) × a).
4775 := (((aaa + aaa) × (aa + aa) − aa × aa)/a + aa + a)/a.
4776 := (((aaa+aaa)×(aa+aa)−aa×aa)/a+aa+a+a)/a.
4777 := ((aa−a−a)×aaa+aaaa×(aa+a))/((a+a+a)×a).
4778 := (((aa − a − a) × aaa + aaaa × (aa + a))/(a + a +
a) + a)/a.
4779 := ((aaaa+aaaa+aa)×(aa+aa+a)/aa+aaa−a)/a.
4780 := ((aaaa + aaaa + aa) × (aa + aa + a)/aa + aaa)/a.
4781 := (((aaa + aaa) × (aa + aa − a) + aa × aa)/a + a +
a + a)/a.
4782 := (((aaa+aaa)×(aa+aa−a)+aa×aa)/a+a+a)/a.
4783 := ((aaa + aaa) × (aa + aa − a) + aa × aa)/(a × a).
4784 := (((aaa + aaa) × (aa + aa − a) + aa × aa)/a + a)/a.
4785 := ((aaa + a) × aaaa/(a + a) − aa)/(aa + a + a).
4786 := ((aaa + a) × aaaa/(a + a) + a + a)/(aa + a + a).
4787 := ((aaa+aa+aa)×(aaa−a−a−a)/(a+a+a)−a)/a.
4788 := (aaa+aa+aa)×(aaa−a−a−a)/((a+a+a)×a).
4789 := ((aaa+aa+aa)×(aaa−a−a−a)/(a+a+a)+a)/a.
4790 := ((aaaa + aa) × aaa/(a + a) − a)/(aa + a + a).
40
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4791 := ((aaaa + a) × (aaa + a)/(a + a) + aa)/(aa + a + a).
4792 := ((aa+aa+aa+aa)×(aaa−a−a)/a−a−a−a−a)/a.
4793 := ((aa+aa+aa+aa)×(aaa−a−a)/a−a−a−a)/a.
4794 := ((aa + aa + aa + aa) × (aaa − a − a)/a − a − a)/a.
4795 := ((aa + aa + aa + aa) × (aaa − a − a)/a − a)/a.
4796 := (aa + aa + aa + aa) × (aaa − a − a)/(a × a).
4797 := ((aa + aa + aa + aa) × (aaa − a − a)/a + a)/a.
4798 := ((aa + aa + aa + aa) × (aaa − a − a)/a + a + a)/a.
4799 := ((aa+aa+aa+aa)×(aaa−a−a)/a+a+a+a)/a.
4800 := (aaaa/aa − (aa − a)/(a + a)) × (aaa − aa)/(a + a).
4801 := ((aaaa + aa) × aaa/(a + a) − a)/(aa + a + a) + aa/a.
4802 := ((aa + aa + aa + aa − a) × (aaa + a)/a − aa − a −
a − a)/a.
4803 := ((aa+aa+aa+aa−a)×(aaa+a)/a−aa−a−a)/a.
4804 := ((aa + aa + aa + aa − a) × (aaa + a)/a − aa − a)/a.
4805 := ((aa + aa + aa + aa − a) × (aaa + a)/a − aa)/a.
4806 := ((aaaa−a)×(aa+a+a)/(a+a+a)−a−a−a−a)/a.
4807 := ((aaaa − a) × (aa + a + a)/(a + a + a) − a − a − a)/a.
4808 := ((aaaa − a) × (aa + a + a)/(a + a + a) − a − a)/a.
4809 := ((aaaa − a) × (aa + a + a)/(a + a + a) − a)/a.
4810 := (aaaa − a) × (aa + a + a)/((a + a + a) × a).
4811 := ((aaaa − a) × (aa + a + a)/(a + a + a) + a)/a.
4812 := ((aaaa + a + a) × (aa + a + a)/(a + a + a) − aa)/a.
4813 := ((aaaa+a+a)×(aa+a+a)/(a+a+a)−aa+a)/a.
4814 := ((aa + aa + aa + aa − a) × (aaa + a)/a − a − a)/a.
4815 := ((aa + aa + aa + aa − a) × (aaa + a)/a − a)/a.
4816 := (aa + aa + aa + aa − a) × (aaa + a)/(a × a).
4817 := ((aaa + aaa − a − a − a) × (aa + aa)/a − a)/a.
4818 := (aaa + aaa − a − a − a) × (aa + aa)/(a × a).
4819 := ((aaa + aaa − a − a − a) × (aa + aa)/a + a)/a.
4820 := ((aaa + aaa − a − a − a) × (aa + aa)/a + a + a)/a.
4821 := ((aaaa + a + a) × (aa + a + a)/(a + a + a) − a − a)/a.
4822 := ((aaaa + a + a) × (aa + a + a)/(a + a + a) − a)/a.
4823 := (aaaa + a + a) × (aa + a + a)/((a + a + a) × a).
4824 := (aaaaaa − aaa − a − a)/(aa + aa + a) − (a + a)/a.
4825 := (aaaaaa − aaa − a − a)/(aa + aa + a) − a/a.
4826 := (aaaaaa − aaa − a − a)/(aa + aa + a).
4827 := (aaaaaa − aaa − a − a)/(aa + aa + a) + a/a.
4828 := (aaaaaa + a + a)/(aa + aa + a) − (a + a + a)/a.
4829 := (aaaaaa + a + a)/(aa + aa + a) − (a + a)/a.
4830 := (aaaaaa − aa − aa + a)/(aa + aa + a).
4831 := (aaaaaa + a + a)/(aa + aa + a).
4832 := (aaaaaa + a + a)/(aa + aa + a) + a/a.
4833 := (aaaaaa + a + a)/(aa + aa + a) + (a + a)/a.
4834 := (aaaaaa + a + a)/(aa + aa + a) + (a + a + a)/a.
4835 := (aaaaaa + a + a)/(aa + aa + a) + (a + a + a + a)/a.
4836 := (aaaaaa + a + a)/(aa + aa + a) + (aa − a)/(a + a).
4837 := (aaaaaa + a + a)/(aa + aa + a) + (aa + a)/(a + a).
4838 := ((aaa + aaa − a − a) × (aa + aa)/a − a − a)/a.
4839 := ((aaa + aaa − a − a) × (aa + aa)/a − a)/a.
4840 := (aaa + aaa − a − a) × (aa + aa)/(a × a).
4841 := ((aaa + aaa − a − a) × (aa + aa)/a + a)/a.
4842 := ((aaa + aaa − a − a) × (aa + aa)/a + a + a)/a.
4843 := ((aaa + aaa − a − a) × (aa + aa)/a + a + a + a)/a.
4844 := (aaaa + aaa − aa) × (aa + a)/((a + a + a) × a).
4845 := ((aaaa + aaa − aa) × (aa + a)/(a + a + a) + a)/a.
4846 := ((aaaa+aaa−aa)×(aa+a)/(a+a+a)+a+a)/a.
4847 := ((aaaa + aaaa) × (aa + aa + a + a)/aa − a)/a.
4848 := aaaa × (aa + a) × (aa + a)/(aa × (a + a + a) × a).
4849 := (aaaa+aa−a−a−a)×(aa+a+a)/((a+a+a)×a).
4850 := (aaaaaa/(aa + aa − a) × aa − a)/(aa + a).
4851 := (aaaaaa/(aa + aa − a) × aa + aa)/(aa + a).
4852 := ((aaa + aaa − aa) × (aa + aa + a)/a − a)/a.
4853 := (aaa + aaa − aa) × (aa + aa + a)/(a × a).
4854 := ((aaa + aaa − aa) × (aa + aa + a)/a + a)/a.
4855 := ((aaa + aaa − aa) × (aa + aa + a)/a + a + a)/a.
4856 := ((aaa + aaa − aa) × (aa + aa + a)/a + a + a + a)/a.
4857 := ((aaa+aaa−a)×(aa+aa)/a−a−a−a−a−a)/a.
4858 := ((aaa + aaa − a) × (aa + aa)/a − a − a − a − a)/a.
4859 := ((aaa + aaa − a) × (aa + aa)/a − a − a − a)/a.
4860 := ((aaa + aaa − a) × (aa + aa)/a − a − a)/a.
4861 := ((aaa + aaa − a) × (aa + aa)/a − a)/a.
4862 := (aaa + aaa − a) × (aa + aa)/(a × a).
4863 := ((aaa + aaa − a) × (aa + aa)/a + a)/a.
4864 := ((aaa + aaa − a) × (aa + aa)/a + a + a)/a.
4865 := ((aaa + aaa − a) × (aa + aa)/a + a + a + a)/a.
4866 := ((aaa + aaa − a) × (aa + aa)/a + a + a + a + a)/a.
4867 := ((aaa+aaa−a)×(aa+aa)/a+a+a+a+a+a)/a.
4868 := ((aaa+aaa)×(aa+aa)/a−aa−a−a−a−a−a)/a.
4869 := ((aaa + aaa) × (aa + aa)/a − aa − a − a − a − a)/a.
4870 := ((aaaa − a − a) × aaaa/aa + a)/(aa + aa + a).
4871 := (aaaaa − aaa × aaa/(aa − a − a))/(a + a).
4872 := ((aaa + aaa + aaa + aaa − a) × aa/a − a)/a.
4873 := (aaa + aaa + aaa + aaa − a) × aa/(a × a).
4874 := ((aaa + aaa + aaa + aaa − a) × aa/a + a)/a.
4875 := ((aaa + aaa) × (aa + aa)/a + a + a − aa)/a.
4876 := ((aaa + aaa) × (aa + aa)/a + a + a − aa + a)/a.
4877 := ((aaa + aaa) × (aa + aa)/a + a + a − aa + a + a)/a.
4878 := (aaa + aaa) × (aa + aa)/(a × a) − (aa + a)/(a + a).
4879 := ((aaa + aaa) × (aa + aa)/a − a − a − a − a − a)/a.
4880 := ((aaa + aaa) × (aa + aa)/a − a − a − a − a)/a.
4881 := ((aaa + aaa) × (aa + aa)/a − a − a − a)/a.
4882 := ((aaa + aaa) × (aa + aa)/a − a − a)/a.
4883 := ((aaa + aaa) × (aa + aa)/a − a)/a.
4884 := (aaa + aaa) × (aa + aa)/(a × a).
4885 := ((aaa + aaa) × (aa + aa)/a + a)/a.
4886 := ((aaa + aaa) × (aa + aa)/a + a + a)/a.
4887 := ((aaa + aaa) × (aa + aa)/a + a + a + a)/a.
4888 := (aaaa + aaa) × (aa + a)/((a + a + a) × a).
4889 := (aaaaa − aaaa − aaa − aaa)/(a + a).
4890 := ((aaaa + aaa) × (aa + a)/(a + a + a) + a + a)/a.
4891 := ((aaaa + aaa + a) × (aa + a)/(a + a + a) − a)/a.
4892 := (aaaa + aaa + a) × (aa + a)/((a + a + a) × a).
4893 := (aaa + aaa + aa) × (aa + aa − a)/(a × a).
4894 := (aaaaa − (aaa + a) × aaa/(a + a) − a)/a.
4895 := (aaaaa − (aaa + a) × aaa/(a + a))/a.
4896 := (aaaaa − (aaa + a) × aaa/(a + a) + a)/a.
4897 := (aaaaa − (aaa + a) × aaa/(a + a) + a + a)/a.
4898 := ((aaa − aa − a − a − a) × aaaa/aa − a)/(a + a).
4899 := (aaaaa − aaaa)/(a + a) − aaaa/aa.
4900 := (aaaa+aaa+a+a+a)×(aa+a)/((a+a+a)×a).
4901 := (aaaa+aa+aa−a−a)×(aa+a+a)/((a+a+a)×a).
4902 := ((aaa + aaa + a) × (aa + aa)/a − a − a − a − a)/a.
4903 := ((aaa + aaa + a) × (aa + aa)/a − a − a − a)/a.
4904 := ((aaa + aaa + a) × (aa + aa)/a − a − a)/a.
4905 := ((aaa + aaa + a) × (aa + aa)/a − a)/a.
4906 := (aaa + aaa + a) × (aa + aa)/(a × a).
4907 := ((aaa + aaa + a) × (aa + aa)/a + a)/a.
4908 := ((aaa + aaa + a) × (aa + aa)/a + a + a)/a.
4909 := ((aaa + aaa + a) × (aa + aa)/a + a + a + a)/a.
4910 := ((aaa + aaa + a) × (aa + aa)/a + a + a + a + a)/a.
4911 := ((aaa + aa + aa) × aaa/(a + a + a) − aa + a)/a.
4912 := ((aaa + aa + aa) × aaa/(a + a + a) − aa + a + a)/a.
4913 := ((aaa + aaa + aa + a) × (aa + aa − a)/a − a)/a.
4914 := (aaa + aaa + aa + a) × (aa + aa − a)/(a × a).
4915 := ((aaa + aaa + aa + a) × (aa + aa − a)/a + a)/a.
4916 := ((aaa + aaa + a) × (aa + aa)/a + aa − a)/a.
4917 := ((aaa + aaa + a) × (aa + aa)/a + aa)/a.
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
4918 := ((aaa + aaa + a) × (aa + aa)/a + aa + a)/a.
4919 := ((aaa + aa + aa) × aaa/(a + a + a) − a − a)/a.
4920 := ((aaa + aa + aa) × aaa/(a + a + a) − a)/a.
4921 := (aaa + aa + aa) × aaa/((a + a + a) × a).
4922 := ((aaa + aa + aa) × aaa/(a + a + a) + a)/a.
4923 := ((aaa + aa + aa) × aaa/(a + a + a) + a + a)/a.
4924 := ((aaa + aa + aa) × aaa/(a + a + a) + a + a + a)/a.
4925 := ((aaa + aaa + a + a) × (aa + aa)/a − a − a − a)/a.
4926 := ((aaa + aaa + a + a) × (aa + aa)/a − a − a)/a.
4927 := ((aaa + aaa + a + a) × (aa + aa)/a − a)/a.
4928 := (aaa + aaa + a + a) × (aa + aa)/(a × a).
4929 := ((aaa + aaa + a + a) × (aa + aa)/a + a)/a.
4930 := ((aaa + aaa + a + a) × (aa + aa)/a + a + a)/a.
4931 := ((aaa + aaa + a + a) × (aa + aa)/a + a + a + a)/a.
4932 := (aaaa + aaa + aa) × (aa + a)/((a + a + a) × a).
4933 := ((aaaa + aaa + aa) × (aa + a)/(a + a + a) + a)/a.
4934 := (aaaaa − aaaa − aaa + a)/(a + a) − aa/a.
4935 := (aaa + aaa + aa + a + a) × (aa + aa − a)/(a × a).
4936 := (aaaa + aaa + aa + a) × (aa + a)/((a + a + a) × a).
4937 := ((aaaa − aa) × aa/(a + a) − aaaa − a − a)/a.
4938 := ((aaaa − aa) × aa/(a + a) − aaaa − a)/a.
4939 := ((aaaa − aa) × aa/(a + a) − aaaa)/a.
4940 := ((aaaa − aa) × aa/(a + a) − aaaa + a)/a.
4941 := ((aaaa − aa) × aa/(a + a) − aaaa + a + a)/a.
4942 := (aaaaa − aaaa − aaa − a)/(a + a) − (a + a)/a.
4943 := (aaaaa − aaaa − aaa − a − a − a)/(a + a).
4944 := (aaaaa − aaaa − aaa − a)/(a + a).
4945 := (aaaaa − aaaa − aaa + a)/(a + a).
4946 := (aaaaa − aaaa − aaa + a + a + a)/(a + a).
4947 := ((aaa − aa − a − a) × aaaa/(aa + aa) − a − a)/a.
4948 := ((aaa − aa − a − a) × aaaa/(aa + aa) − a)/a.
4949 := (aaa − aa − a − a) × aaaa/(aa × (a + a)).
4950 := (aaaaa − aaaa − aaa + aa)/(a + a).
4951 := (aaaaa − aaaa − aaa + aa + a + a)/(a + a).
4952 := ((aaaa − aa) × aa/(a + a) − aaaa + aa + a + a)/a.
4953 := (aaaaa − aaaa − aaa − a)/(a + a) + (aa − a − a)/a.
4954 := (aaaaa − aaaa − aaa − a)/(a + a) + (aa − a)/a.
4955 := (aaaaa − aaaa − aaa − a)/(a + a) + aa/a.
4956 := ((aaa + aa + aa + a) × aaa/(a + a + a) − a − a)/a.
4957 := ((aaa + aa + aa + a) × aaa/(a + a + a) − a)/a.
4958 := (aaa + aa + aa + a) × aaa/((a + a + a) × a).
4959 := ((aaaa − aaa + a) × (aaa − a − a)/aa − a)/(a + a).
41
4960 := ((aaa − aa − a − a) × aaaa/(aa + aa) + aa)/a.
4961 := ((aa + aa + aa + aa) × (aaa + a + a)/a − aa)/a.
4962 := ((aa + aa + aa + aa) × (aaa + a + a)/a − aa + a)/a.
4963 := (aaaaa − aaaa)/(a + a) − aaa/(a + a + a).
4964 := (aaaaa − aaaa)/(a + a) − aaa/(a + a + a) + a/a.
4965 := (aaaaa−aaaa)/(a+a)−aaa/(a+a+a)+(a+a)/a.
4966 := (aaaaa − aaaa)/(a + a) − (aa + aa + aa + a)/a.
4967 := ((aaaa × (a + a + a)/aa + aaa) × (aa + a)/a − a)/a.
4968 := (aaaa × (a + a + a)/aa + aaa) × (aa + a)/(a × a).
4969 := ((aa+aa+aa+aa)×(aaa+a+a)/a−a−a−a)/a.
4970 := ((aa + aa + aa + aa) × (aaa + a + a)/a − a − a)/a.
4971 := ((aa + aa + aa + aa) × (aaa + a + a)/a − a)/a.
4972 := (aa + aa + aa + aa) × (aaa + a + a)/(a × a).
4973 := ((aa + aa + aa + aa) × (aaa + a + a)/a + a)/a.
4974 := ((aa + aa + aa + aa) × (aaa + a + a)/a + a + a)/a.
4975 := ((aa+aa+aa+aa)×(aaa+a+a)/a+a+a+a)/a.
4976 := (aaaa + aaa + aa + aa) × (aa + a)/((a + a + a) × a).
4977 := (aaaaa − aaaa)/(a + a) − (aa + aa + a)/a.
4978 := (aaaaa − aaaa)/(a + a) − (aa + aa)/a.
4979 := (aaaaa − aaaa)/(a + a) − (aa + aa − a)/a.
4980 := (aaaaa − aaaa)/(a + a) − (aa + aa − a − a)/a.
4981 := ((aaaa − a) × aa/(a + a) − aaaa − a − a − aa)/a.
4982 := (aaaaa − aaaa − aa − aa − aa − a)/(a + a) − a/a.
4983 := (aaaaa − aaaa − aa − aa − aa − a)/(a + a).
4984 := ((aaaa − a) × aa/(a + a) − aaaa + a − aa)/a.
4985 := ((aaa + aaa) × (aa + aa + a) − aa × aa)/(a × a).
4986 := (aaaaa − aaaa)/(a + a) − (aa + a + a + a)/a.
4987 := (aaaaa − aaaa)/(a + a) − (aa + a + a)/a.
4988 := (aaaaa − aaaa)/(a + a) − (aa + a)/a.
4989 := (aaaaa − aaaa)/(a + a) − aa/a.
4990 := (aaaaa − aaaa)/(a + a) − (aa − a)/a.
4991 := (aaaaa − aaaa)/(a + a) − (aa − a − a)/a.
4992 := ((aaaa − a) × aa/(a + a) − aaaa − a − a)/a.
4993 := (aaaaa − aaaa − aa − a − a − a)/(a + a).
4994 := ((aaaa − a) × aa/(a + a) − aaaa)/a.
4995 := ((aaaa − a) × aa/(a + a) − aaaa + a)/a.
4996 := (aaaaa − aaaa)/(a + a) − (a + a + a + a)/a.
4997 := (aaaaa − aaaa)/(a + a) − (a + a + a)/a.
4998 := (aaaaa − aaaa)/(a + a) − (a + a)/a.
4999 := (aaaaa − aaaa − a − a)/(a + a).
5000 := (aaaaa − aaaa)/(a + a).
3. Single Letter Representations Using Potentiation
In this section, we have given some examples having potentiation. In some cases, this operation reduces the numbers of
letters a, but there are only few examples. Here we considered the results upto 10000.
Power 2.
4 := 22 = ((a + a)/a)(a+a)/a .
9 := 32 = ((a + a + a)/a)(a+a)/a .
16 := 42 = ((a + a + a + a)/a)(a+a)/a .
25 := 52 = ((aa − a)/(a + a))(a+a)/a .
36 := 62 = ((aa + a)/(a + a))(a+a)/a .
49 := 72 = ((aa − a − a − a − a)/a)(a+a)/a .
64 := 82 = ((aa − a − a − a)/a)(a+a)/a .
81 := 92 = ((aa − a − a)/a)(a+a)/a .
100 := 102 = ((aa − a)/a)(a+a)/a .
121 := 112 = (aa/a)(a+a)/a .
144 := 122 = ((aa + a)/a)(a+a)/a .
169 := 132 = ((aa + a + a)/a)(a+a)/a .
196 := 142 = ((aa + a + a + a)/a)(a+a)/a .
225 := 152 = ((aa + a + a + a + a)/a)(a+a)/a .
256 := 162 = ((aa + a + a + a + a + a)/a)(a+a)/a .
289 := 172 = ((aa + a)/(a + a) + aa/a)(a+a)/a .
324 := 182 = ((aa − a − a) × (a + a)/(a × a))(a+a)/a .
361 := 192 = ((aa + aa − a − a − a)/a)(a+a)/a .
400 := 202 = ((aa + aa − a − a)/a)(a+a)/a .
441 := 212 = ((aa + aa − a)/a)(a+a)/a .
484 := 222 = ((aa + aa)/a)(a+a)/a .
529 := 232 = ((aa + aa + a)/a)(a+a)/a .
576 := 242 = ((aa + aa + a + a)/a)(a+a)/a .
625 := 252 = ((aa + aa + a + a + a)/a)(a+a)/a .
676 := 262 = ((aa + a + a) × (a + a)/(a × a))(a+a)/a .
729 := 272 = (((aa + a + a) × (a + a)/a + a)/a)(a+a)/a .
784 := 282 = ((aaa + a)/(a + a + a + a))(a+a)/a .
841 := 292 = (((aa − a) × (a + a + a)/a − a)/a)(a+a)/a .
900 := 302 = ((aa − a) × (a + a + a)/(a × a))(a+a)/a .
961 := 312 = ((aa + aa + aa − a − a)/a)(a+a)/a .
1024 := 322 = ((aa + aa + aa − a)/a)(a+a)/a .
42
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
1089 := 332
1056 := 342
1225 := 352
1296 := 362
1369 := 372
1444 := 382
1521 := 392
1600 := 402
1681 := 412
1764 := 422
1849 := 432
1936 := 442
2025 := 452
2116 := 462
2209 := 472
2304 := 482
2401 := 492
2500 := 502
2601 := 512
2704 := 522
2809 := 532
2916 := 542
3025 := 552
3136 := 562
3249 := 572
3364 := 582
3481 := 592
3600 := 602
3721 := 612
3844 := 622
3969 := 632
4096 := 642
4225 := 652
4356 := 662
4489 := 672
4624 := 682
4761 := 692
4900 := 702
5041 := 712
5184 := 722
5329 := 732
5476 := 742
5625 := 752
5776 := 762
5929 := 772
6084 := 782
6241 := 792
6400 := 802
6561 := 812
6724 := 822
6889 := 832
7056 := 842
7225 := 852
7396 := 872
7569 := 872
7744 := 882
= ((aa + aa + aa)/a)(a+a)/a .
= ((aa + aa + aa + a)/a)(a+a)/a .
= ((aa + aa + aa + a + a)/a)(a+a)/a .
= ((aa + a) × (a + a + a)/(a × a))(a+a)/a .
= (aaa/(a + a + a))(a+a)/a .
= (aaa/(a + a + a) + a/a)(a+a)/a .
= ((aa + a + a) × (a + a + a)/(a × a))(a+a)/a .
= ((a + a + a + a) × (aa − a)/(a × a))(a+a)/a .
= ((aaa + aa + a)/(a + a + a))(a+a)/a .
= ((aa + aa − a) × (a + a)/(a × a))(a+a)/a .
= (((a + a + a + a) × aa/a − a)/a)(a+a)/a .
= ((a + a + a + a) × aa/(a × a))(a+a)/a .
= (((a + a + a + a) × aa/a + a)/a)(a+a)/a .
= ((aa + aa + a) × (a + a)/(a × a))(a+a)/a .
= (((aa + aa + a) × (a + a)/a + a)/a)(a+a)/a .
= ((a + a + a + a) × (aa + a)/(a × a))(a+a)/a .
= ((aaa − aa − a − a)/(a + a))(a+a)/a .
= ((aaa − aa)/(a + a))(a+a)/a .
= ((aaa − aa + a + a)/(a + a))(a+a)/a .
= ((aaa − aa)/(a + a) + (a + a)/a)(a+a)/a .
= ((aaa − a)/(a + a) − (a + a)/a)(a+a)/a .
= ((aaa − a − a − a)/(a + a))(a+a)/a .
= ((aaa − a)/(a + a))(a+a)/a .
= ((aaa + a)/(a + a))(a+a)/a .
= ((aaa + a + a + a)/(a + a))(a+a)/a .
= ((aaa + a)/(a + a) + (a + a)/a)(a+a)/a .
= (((aa × aa − a × a)/(a + a) − a)/a)(a+a)/a .
= ((aa × aa/a − a)/(a + a))(a+a)/a .
= ((aaa + aa)/(a + a))(a+a)/a .
= ((aaa + aa + a + a)/(a + a))(a+a)/a .
= ((aa + aa − a) × (a + a + a)/(a × a))(a+a)/a .
= (((aa + a) × aa/(a + a) − a − a)/a)(a+a)/a .
= (((aa + a) × aa/(a + a) − a)/a)(a+a)/a .
= ((aa + a) × aa/((a + a) × a))(a+a)/a .
= ((aaa + aa + aa + a)/(a + a))(a+a)/a .
= (((aa + a) × aa/(a + a) + a + a)/a)(a+a)/a .
= ((aa + aa + a) × (a + a + a)/(a × a))(a+a)/a .
= (((aa + a) × (aa + a)/(a + a) − a − a)/a)(a+a)/a .
= (((aa + a) × (aa + a)/(a + a) − a)/a)(a+a)/a .
= ((aa + a) × (aa + a)/((a + a) × a))(a+a)/a .
= ((aaa/(a + a + a) × (a + a) − a)/a)(a+a)/a .
= (aaa/(a + a + a) × (a + a)/a)(a+a)/a .
= ((aaa/(a + a + a) × (a + a) + a)/a)(a+a)/a .
= (((aa − a − a − a − a) × aa/a − a)/a)(a+a)/a .
= ((aa − a − a − a − a) × aa/(a × a))(a+a)/a .
= ((aaa − aa − aa − aa)/a)(a+a)/a .
= ((aaa − aa − aa − aa + a)/a)(a+a)/a .
= ((aa − a − a − a) × (aa − a)/(a × a))(a+a)/a .
= ((aa − a − a) × (aa − a − a)/(a × a))(a+a)/a .
= (((aa − a − a) × (aa − a − a)/a + a)/a)(a+a)/a .
= (((aa + a) × (aa + a)/(a + a) + aa)/a)(a+a)/a .
= ((a + a + a + a) × (aa + aa − a)/(a × a))(a+a)/a .
= ((aaa/(a + a + a) × (a + a) + aa)/a)(a+a)/a .
= ((aaa − aa − aa − a − a − a)/a)(a+a)/a .
= ((aaa − aa − aa − a − a)/a)(a+a)/a .
= ((aaa − aa − aa − a)/a)(a+a)/a .
7921 := 892 = ((aaa − aa − aa)/a)(a+a)/a .
8100 := 902 = ((aaa − aa − aa + a)/a)(a+a)/a .
8281 := 912 = ((aaa − aa − aa + a + a)/a)(a+a)/a .
8464 := 922 = ((aaa − aa − aa + a + a + a)/a)(a+a)/a .
8649 := 932 = (((a − aa + a) × (a + a)/a + aaa)/a)(a+a)/a .
8836 := 942 = ((aaaa + aaa)/(aa + a + a))(a+a)/a .
9025 := 952 = ((aaa − aa − a − a − a − a − a)/a)(a+a)/a .
9216 := 962 = ((aaa − aa − a − a − a − a)/a)(a+a)/a .
9409 := 972 = ((aaa − aa − a − a − a)/a)(a+a)/a .
9604 := 982 = ((aaa − aa − a − a)/a)(a+a)/a .
9801 := 992 = ((aaa − aa − a)/a)(a+a)/a .
10000 := 1002 = ((aaa − aa)/a)(a+a)/a .
Power 3.
8 := 23 = ((a + a)/a)(a+a+a)/a .
27 := 33 = ((a + a + a)/a)(a+a+a)/a .
64 := 43 = ((a + a + a + a)/a)(a+a+a)/a .
125 := 53 = ((aa − a)/(a + a))(a+a+a)/a .
216 := 63 = ((aa + a)/(a + a))(a+a+a)/a .
343 := 73 = ((aa − a − a − a − a)/a)(a+a+a)/a .
512 := 83 = ((aa − a − a − a)/a)(a+a+a)/a .
729 := 93 = ((aa − a − a)/a)(a+a+a)/a .
1000 := 103 = ((aa − a)/a)(a+a+a)/a .
1331 := 113 = (aa/a)(a+a+a)/a .
1728 := 123 = ((aa + a)/a)(a+a+a)/a .
2197 := 133 = ((aa + a + a)/a)(a+a+a)/a .
2744 := 143 = ((aa + a + a + a)/a)(a+a+a)/a .
3375 := 153 = ((aa + a + a + a + a)/a)(a+a+a)/a .
4096 := 163 = ((aa + a + a + a + a + a)/a)(a+a+a)/a .
4913 := 173 = ((aa + a)/(a + a) + aa/a)(a+a+a)/a .
5832 := 183 = ((aa − a − a) × (a + a)/(a × a))(a+a+a)/a .
6859 := 193 = ((aa + aa − a − a − a)/a)(a+a+a)/a .
8000 := 203 = ((aa + aa − a − a)/a)(a+a+a)/a .
Power of 2.
4 := 22 = ((a + a)/a)(a+a)/a .
8 := 23 = ((a + a)/a)(a+a+a)/a .
16 := 24 = ((a + a)/a)(a+a+a+a)/a .
32 := 25 = ((a + a)/a)(aa−a)/(a+a) .
64 := 26 = ((a + a)/a)(aa+a)/(a+a) .
128 := 27 = ((a + a)/a)(aa−a−a−a−a)/a .
256 := 28 = ((a + a)/a)(aa−a−a−a)/a .
512 := 29 = ((a + a)/a)(aa−a−a)/a .
1024 := 210 = ((a + a)/a)(aa−a)/a .
2048 := 211 = ((a + a)/a)( aa/a).
4096 := 212 = ((a + a)/a)(aa+a)/a .
8192 := 213 = ((a + a)/a)(aa+a+a)/a .
Power of 3.
9 := 32 = ((a + a + a)/a)(a+a)/a .
27 := 33 = ((a + a + a)/a)(a+a+a)/a .
81 := 34 = ((a + a + a)/a)(a+a+a+a)/a .
243 := 35 = ((a + a + a)/a)(aa−a)/(a+a) .
729 := 36 = ((a + a + a)/a)(aa+a)/(a+a) .
2187 := 37 = ((a + a + a)/a)(aa−a−a−a−a)/a .
6561 := 38 = ((a + a + a)/a)(aa−a−a−a)/a .
3.1. Comparison Results. Comparing to the numbers appearing in Section 3, there are very few numbers with power having
better representations. Here below are these representations:
16 := ((a + a + a + a)/a)(a+a)/a .
27 := ((a + a + a)/a)(a+a+a)/a .
64 := ((a + a)/a)(aa+a)/(a+a) .
81 := ((aa − a − a)/a)(a+a)/a .
128 := ((a + a)/a)(aa+a+a)/(a+a) .
144 := ((aa + a)/a)(a+a)/a .
169 := ((aa + a + a)/a)(a+a)/a .
196 := ((aa + a + a + a)/a)(a+a)/a .
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
43
2025 := (((a + a + a + a) × aa/a + a)/a)(a+a)/a .
2048 := ((a + a)/a)( aa/a).
2116 := ((aa + aa + a) × (a + a)/(a × a))(a+a)/a .
2187 := ((a + a + a)/a)(aa−a−a−a−a)/a .
2197 := ((aa + a + a)/a)(a+a+a)/a .
2304 := ((a + a + a + a) × (aa + a)/(a × a))(a+a)/a .
2401 := ((aaa − aa − a − a)/(a + a))(a+a)/a .
2500 := ((aaa − aa)/(a + a))(a+a)/a .
2601 := ((aaa − aa + a + a)/(a + a))(a+a)/a .
2704 := ((aaa − aa)/(a + a) + (a + a)/a)(a+a)/a .
2744 := ((aa + a + a + a)/a)(a+a+a)/a .
2809 := ((aaa − a)/(a + a) − (a + a)/a)(a+a)/a .
2916 := ((aaa − a − a − a)/(a + a))(a+a)/a .
3025 := ((aaa − a)/(a + a))(a+a)/a .
3136 := ((aaa + a)/(a + a))(a+a)/a .
3249 := ((aaa + a + a + a)/(a + a))(a+a)/a .
3364 := ((aaa + a)/(a + a) + (a + a)/a)(a+a)/a .
3481 := (((aa × aa − a × a)/(a + a) − a)/a)(a+a)/a .
3600 := ((aa × aa/a − a)/(a + a))(a+a)/a .
3721 := ((aaa + aa)/(a + a))(a+a)/a .
3844 := ((aaa + aa + a + a)/(a + a))(a+a)/a .
3969 := ((aa + aa − a) × (a + a + a)/(a × a))(a+a)/a .
4225 := (((aa + a) × aa/(a + a) − a)/a)(a+a)/a .
4356 := ((aa + a) × aa/((a + a) × a))(a+a)/a .
4489 := ((aaa + aa + aa + a)/(a + a))(a+a)/a .
4624 := (((aa + a) × aa/(a + a) + a + a)/a)(a+a)/a .
4761 := ((aa + aa + a) × (a + a + a)/(a × a))(a+a)/a .
4900 := (((aa + a) × (aa + a)/(a + a) − a − a)/a)(a+a)/a .
216 := ((aa + a)/(a + a))(a+a+a)/a .
256 := ((a + a)/a)(aa−a−a−a)/a .
289 := ((aa + a)/(a + a) + aa/a)(a+a)/a .
343 := ((aa + a + a)/(a + a))(a+a+a)/a .
361 := ((aa + aa − a − a − a)/a)(a+a)/a .
400 := ((aa + aa − a − a)/a)(a+a)/a .
441 := ((aa + aa − a)/a)(a+a)/a .
484 := ((aa + aa)/a)(a+a)/a .
512 := ((a + a)/a)(aa−a−a)/a .
529 := ((aa + aa + a)/a)(a+a)/a .
576 := ((aa + aa + a + a)/a)(a+a)/a .
625 := ((aa + aa + a + a + a)/a)(a+a)/a .
676 := ((aa + a + a) × (a + a)/(a × a))(a+a)/a .
729 := ((a + a + a)/a)(aa+a)/(a+a) .
784 := ((aaa + a)/(a + a + a + a))(a+a)/a .
961 := ((aa + aa + aa − a − a)/a)(a+a)/a .
1024 := ((a + a)/a)(aa−a)/a .
1056 := ((aa + aa + aa + a)/a)(a+a)/a .
1331 := (aa/a)(a+a+a)/a .
1369 := (aaa/(a + a + a))(a+a)/a .
1444 := (aaa/(a + a + a) + a/a)(a+a)/a .
1521 := ((aa + a + a) × (a + a + a)/(a × a))(a+a)/a .
1600 := ((a + a + a + a) × (aa − a)/(a × a))(a+a)/a .
1681 := ((aaa + aa + a)/(a + a + a))(a+a)/a .
1728 := ((aa + a)/a)(a+a+a)/a .
1764 := ((aa + aa − a) × (a + a)/(a × a))(a+a)/a .
1849 := (((a + a + a + a) × aa/a − a)/a)(a+a)/a .
1936 := ((a + a + a + a) × aa/(a × a))(a+a)/a .
4. Final Comments and Historical Notes
This work on representations of natural numbers using single letter is first of its kind. It is revision over author’s [14]
previous work, where the results goes up to 3000. Here, the representations from 0 to 5000. More than half numbers are
calculated manually. By no mean we can say that the above representations are unique. The previous work [14] also brings
interesting connections with palindromic and number patterns. This we have separated, and can be seen in [16].
Author [11] also worked with representation of numbers using single digit separately for each value from 1 to 9. Representations of numbers using all the digits from 1 to 9, in increasing and decreasing orders is done by the author [9].
Comments to this work can be seen at [1, 2, 7, 8]. Different study on numbers, such as, selfie numbers, running expressions,
etc. refer to author’s work [10, 12, 13, 15]. For historical point of view, we suggest [3, 4, 5, 6].
Acknowledgement
The author is thankful to T.J. Eckman, Georgia, USA (email: [email protected]) in programming the script to develop these
representations.
References
[1] ABRAHAMS, M, Lots of numbers, plain and almost simple, IMPROBABLE RESEACH, http://www.improbable.com/2013/02/12/lots-of-numbersplain-and-almost-simple.
[2] ABRAHAMS, M, Lots more numbers, deemed ”crazy consecutive”, IMPROBABLE RESEACH, http://www.improbable.com/2013/06/08/lots-morenumbers-deemed-crazy-consecutive.
[3] DUDENEY, H.E., Amusements in Mathematics, EBD E-Books Directory.com, 1917.
[4] FREIDMAN, E., Problems of the Month (December 1999), http://www2.stetson.edu/ efriedma/mathmagic/1299.html
[5] HEINZ, H. ”Number Patterns.http://www.magic-squares.net/.
[6] MADACHY, J.S., Mathematics on Vacations, Charlers Scriber’s Son, New York, 1966.
[7] NEBUS, J., Counting To 52, nebusresearch, http://nebusresearch.wordpress.com/2013/02/17/counting-to-52/.
[8] NEBUS, J., Counting From 52 to 11,108, nebusresearch, http://nebusresearch.wordpress.com/2013/06/10/counting-from-52-to-11108/.
[9] TANEJA, I.J., Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9,
http://arxiv.org/abs/1302.1479.
44
SINGLE LETTER REPRESENTATIONS - INDER J. TANEJA
[10] TANEJA, I.J., Selfie Numbers: Consecutive Representations in Increasing and Decreasing Orders, RGMIA Research Report Collection, 17(2014),
Article 140, pp. 1-57. http://rgmia.org/papers/v17/v17a140.pdf, 2014.
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