Math 222A W03 D. Congruence relations 1 . The concept Let`s start

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mi=#-u2K5DCE-uT#-‰eO#:<.>:HNDOW9$NP74Š„2‹@xNP7;58FHQP-/a#7>5D:GI24Œq2`.>-1CS2‹:HOvQP-1Oh-17>58FL
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{ Á } NP7 {[|Ã} ºBÁ ¼ ^ š FG2KN#f9-vCY5JŒÄ2>5JŒ*Å4I/NPO#QP74R#-1O#I/-1ÆÇ:HO#2`.>-15DT[ND@YÅ4I1NDO#QP7KRh-1O#I/74-1Fs5—.>:HNDO#Æ#^E_DR#24.°5D2w@xNP7u-1p„R#:<r85DFH-/O#I1-S7K-/Fs58.K:HNPO#2w:GOÈQP-1O#-/7>5DF¦f9-SIJ5DOÄ2Kd™-J5DбND@.>=#É ¡H–y›6ÊyË N8@5bI1NDO#QP7KRh-1O#I/-7K-/Fs58.K:HNPOYºBNP7Å4I1FH5D2K24-124Æ#fPa#Rh.n.>=5—.R#2K5DQP-$:G2n24NPCS-/9;=58.NPFHT ¼ ^
ÌNP7 {SÍ ¥°fh.K=#-ua#FHNqI6ŠWND@ { :H2iN8@•.>-1OvI15DFHFG-1TÈ{ Î ^
AÏvÐtMÑ +w!»\%
º Ž ¼ÓÒ OÂZ;f#5¯I/NPO#QP74R#-1OhI1-A7K-1FH58.>:GNPOW:G2.>=#-w2K5DCE-u582‹I/NPO#QP74R#-1OhI1-ACENqT?VÂ@xNP7i2KNDCEVn^‚mi=#-AIJ5D24-AVXjԈo:G2;5DFHFGN­9-1T f#QP:Grq:GO#Qz.>=#-u-/pqR#5DFH:<.´ŒW7K-/Fs58.K:HNPO ^
ºÕ ¼ÓÒ OE5uQP7KNPRhd·fq5AI/NPO#QP74R#-1O#I/-t74-1FH58.>:GNPO¯:H2.>=h-t2K5DCE-i.K=#:HO#QA5D2M.>=h-‹I/NP2K-‰.$Th-1I1NDC¯µ
d™NP24:G.>:GNPOY@xNP7;5¯O#NP74CY58F 2KRha#QP7KNDR#d·^
º¦Ö ¼ÓÒ O²5EI/NPCEC°Rh.658.K:GrD-A74:HO#Qhf5EI1NDO#QP7KRh-1O#I/-°7K-/Fs58.K:HNPOv:G2‹.K=#-(2K5DCS-A.K=#:HO#QE5D2;.>=#I/NP2K-‰.‹T#-1I/NPCEd™NP24:G.>:GNPOW@xNP7;5DOv:GT#-J5DF¦^
ºB× ¼ÓÒ O5ÂeO#:<.>-vI6=5D:GOØ¯f5ÇI/NPO#QP74R#-1O#I/-X74-1FH58.>:GNPO[:H2¯5DO]Œ[Th-1I1NDCEd™NP2K:<.>:GNPO[:HO].>N
:GO].>-17`r85DFH2/f#5D2;:HO‡Ì:GQPR#74- Ž º¦5 ¼ ^
ºÙ ¼ ,\58.4.>:GI1-12i:GOvQP-1O#-/7>5DFI15DO‡=5JrP-AI1NPO#QD7KR#-/O#I1-A7K-/Fs58.K:HNPO#2/f#5D2;:GOvÌ:HQPRh7K- Ž xº a ¼ ^
Ú Ž
º¦k ¼ Ì NP7Y5)=#NPCSNPCSNP7Kdh=#:H24C
Lt£ tf;.K=#-±ŠD-/7KO#-/FND@ :G2?5)I1NDO#QP7KRh-1O#I/74-1FH58.>:GNPO·^
‹-174-.K=#- Ê]‰ž…’ ‰¡ ND@5‹=#NPCSNPCSNP7Kd#=h:H2KC CS-J5DO#2\.>=h--/pqRh:Gr85DFH-/O#I1-M74-1Fs5—.>:HNDOu.K=58.
:HOhT#R#I1-/2(NDOÄ:<.>2uT#NPCE5D:HO L {±| { ~
º {q¼ j º { ~ ¼ ^Ymi=h:H2u:H2A5vI1NPO].>7K5D24.
9;:<.>=z.K=#-i2Kd™-1I/:GeIiI15D2K-/2N8@cQD7KNPR#dh2M5DO#T¯7K:GO#QP21f89;=#-174-;.K=#-iŠD-/7KO#-/F:H2‚5wO#ND7KCE5DF
24R#a#QP74NPR#d·^tNy9$-‰rP-/71f
h5DCSd#FH-Ǻ¦Õ ¼ 24=#Ny9;2S.K=58.z.K=#-?.´9$NÈT#-‰eO#:G.K:HNPOh2¯5D7K-/p„R#:Gr85DFG-1O].J^
º¦5 ¼
ºBa ¼
Ì:HQDR#7K- Ž L$NDO#QP7KRh-1O#I/-(74-1Fs5—.>:HNDO#2NPOvFs5—.K.>:GI1-/2
i(') *n ! q" œ !` Ò .‹:H2i-15D24Œ?.KNE24-1-u.>=5—.b58OX:GO„.K-1742K-1I‰.>:GNPOXN8@I/NPO#QP74R#-1O#I/-°74-1Fs5—.>:HNDO#2NPO‡£ :G2;5DQ]5D:GOX5
I/NPO#QP74R#-1O#I/-E74-1FH58.>:GNPO·^omi=#-/7K-/@xND7K-o.>=#-SI1NDO#QP7KRh-1O#I/-E74-1Fs5—.>:HNDO#2NPOÇ£Ó@xNP74CÃ5vI1NPCoµ
d#FG-/.K-EFH58.K.K:HI1-8f$NPOºB£ ¼ ^ Ò O)@B5DI‰.Jf$NPOºB£ ¼ :H2A2K:GCEd#F<ŒÇ5X24R#a#Fs5—.K.>:GI1-END@‚p„R#:Gr·ºB¥ ¼ ^
NDCE-w-#58CEd#FG-12/L
ºB5 ¼ ÌNP7(5XQD7KNPR#dSfn.>=#-SFs58.4.>:GI1-$NPO\º ¼ :H2A-12K24-1O].>:H5DFHF<Œ±.>=#-E2>5DCS-E.K=#:HOhQ²5D2A.>=#FH58.K.K:HI1-bND@OhNP7KCE5DF·24R#a#QP74NPR#d#2/ftNP74CY5DF¦º ¼ ^
ºxa ¼ ÌND7E5ÈI1NDCECzRU.658.K:GrP-v74:HO#Qzf.K=#-‡Fs58.4.>:HI/-$NPO\º ¼ :G2S-/2K24-1O].>:H5DFHF<Œ.>=#-‡2>58CE.K=#:HO#Q¯582;.K=#-uFs58.4.>:GI1-ND@n:HTh-J5DFG2iND@z^
ºxI ¼ mi=#-uI1NPOhQP7KR#-/O#I1-AFs5—.K.>:GI1-N8@5o@xNPR#7»µ´-1FG-1CS-1O].iI6=58:HO‡:H2.>=h- NUNPFG-J5DO?FH58.K.K:HI/-"!$#J^
&b !` %
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ÌNP7t5YQP74NPR#d(9;:G.K=ÂO#NP74CY58F24R#a#QP74NPR#d*))f9-zIJ5DOX@xNP7KC+ ,-))^tÌND7b5YI/NPCSCzRUµ
.>58.>:<rP-w7K:GO#Q. 9;:<.>=v:HTh-J5DF0/fh9-(I15DO?@xNP7KC1",2/^ Ò OXQP-/O#-17K5DFL
×#^ Žzzx‘M’“•”B“–—’™˜ ÌNP7;5DOX5DFHQP-/a#7>5z£j ¤¦¥°§6¨]©…ªJ«1«J«/ª6¨­¬®;58O#TÂÁ Í $NPO\ºx£ ¼ fFG-/.;£.,DÁ
a™-w.>=#-(5DFHQD-1a#7K5o9;=hNP2K-A-1FG-1CS-1O].>2t5D7K-w.K=#-(ahFHNqI6Šq2;ND@Á¯5DO#TX9;=hNP2K-ANPd™-17>5—.>:HNDO#2‹5D7KT#-‰eO#-/T±5D2;@xNPFHFGN­9;2/LÌND7‹-15DI6=Âa582K:HIuNPd™-17K58.>:GNPO²¨­³nNPO š fT#-/eOh-z5EI/NP7K74-124dcNPOhT#:HO#Q
NPd™-17K58.>:GNPO‡¨­³NPOv£.,DÁza]Œ
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Ú Õ
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i
.K=#-$74-12KRhFG.nT#NU-/2O#N8.T#-/dc-/O#ToNPO(9;=h:HI6=z74-1d#74-12K-/O].658.K:GrP-/2M5D7K-I6=#NP24-1Oz@xNP7\.>=#-a#FHNqI6Є21^
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º {q¼ j {Î ^
ND@£ÃNPO].>NX£.,DÁ‡:G2¶L£ £.,DÁvQP:GrD-1Oa]Œ
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d#=h:H2KC 9;:G.>=vŠ8-17KOh-1FÁU^
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ÁoNPO‡£
£.,DÁ
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d#=h:H2KC‡^
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(') u% " %h Ñ + w" % Ñ
\ Ñ
ÌNP7¯QP74NPR#d#2/f7K-/IJ5DFGF.>=#- Å`e7424.E:H2KNDCENP74d#=#:G2KC.K=#-1ND7K-1CSÆ#L Ò @ L ))f.>=#-/O
:GC j ,8Š8-17 ^ À 7w-/p„R#:Gr85DFG-1O].>F<ŒPf:G@ L ) :G2u5?2KR#74-1I/.K:HNPOÈ9;:G.K=ȊD-174O#-1F
f#.K=#-1O ) j ,^
mi=#:G2.K=#-1NP74-1C :H2R#2K-‰@xR#F·:GOY- h5DCSd#FG-121^ Ò .5DFH24N°24=#Ny9;2$.>=5—.$.>=h-=#NPCSNPCSNP7Kd#=h:HI;:HCoµ
5DQD-12ND@5uQP7KNDR#d 5D74-‹Th-/.>-/7KCS:HO#-/TYR#dS.>NA:H24NPCEND7Kd#=#:G2KCa]Œ¯:[email protected]:HNPOo:GO„.K-174O5DF
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CE5DO]ŒW=#NDCENPCSNP74d#=#:HIb:HCE5DQP-12/^
ÌNP7;5DFGQP-1ah7>5D2:GOvQP-1O#-/7>5DF¦fh.>=h-A24:G.KR58.>:GNPO?:H2.K=#-u2>5DCS-DL
ÙU^ Ž ½ 6–—ž6‰¾ º !"$#&%'#(*)+!,% *+.-/#(*-/% ¼ ^E,-/. L·£ *
ac-S5v=#NPCSN8µ
CSNP7Kdh=#:H24CX^mi=h-1O²:GC 0j ¥ ,8Š8-17 ^‚pqRh:Gr85DFH-/O].>FGŒDf#:G@ L]£ G: 2;5o2KR#74-1I/.K:GrD=#NDCENPCSNP74d#=#:H24C 9;:<.>=vŠD-/7KO#-/FÁUf#.>=h-1O j £.,8ÁU^
Ú*Ö
UÙ ^ Õ –—ž>–—¡•¡<¢Dž…¿P˜ mi=#-wd™NP2K24:Ha#FG-=#NPCSNPCSNP7Kd#=h:HI‹:HCE5DQP-12ND@\£ 5D7K-bT#-/.K-17KCS:HOh-1T?R#d?.>N
:G2KNPCSNP7Kdh=#:H24C a]ŒW.K=#-u:HO].>-/7KO5DF2`.>74R#I/.KR#7K-AND@n£?^
w \ Ñ
(') *\%#+°
À O#-zrD-17K24:HNPOÈ@xNP7QD7KNPR#dh21L Ò @ L ) :H2w5?24R#74-/I/.>:<rP-¯=#NPCSNPCSNP7Kdh=#:H24CXf™.>=#-/O
.K=#-174-:H2‚5tNPO#-‰µ.>N8µ NPO#-I1NP747K-124dcNDO#T#-1OhI1-;ac-‰.´9$-/-1O¯.>=#-$O#NP7KCE5DFq2KR#ahQP7KNPRhd#2‚ND@ ) 5DOhT
.K=#-¯O#NP7KCE5DF24R#a#QP74NPR#d#2AND@ .>=5—.uI1NPO].658:HONJD-17 ^ Ò OÇ@B5DI/.1f.>=#-¯2KRha#QP7KNDR#dÄN8@ I/NP7K74-12Kd™NPO#Th:HO#Qo.>NE5oO#NP74CY5DFc2KR#ahQP7KNPRhd ND@) :G2‹24:HCSd#FGŒ © º, ¼ ^
mi=#-uQP-/O#-17K5DFH:J58.K:HNPOW.KNS5DFHQP-/a#7>582i:H2.>=h:H21L
kh^ Ž ½ 6–—ž>‰¾ º #&**-/$)#
.- - + - #(*- % ¼ ^ Ò @ L„£ l:G2;5S24R#74-/I/.>:<rP-A=#N8µ
CSNPCSNP7Kd#=h:H2KC‡f8.K=#-1OE.>=#-/7K-‹:H25ANDO#-‰µ.>N8µ NPO#-;I1NP747K-/2Kd™NPO#T#-/O#I1-a™-/.´9-1-/OWI1NDO#QP7KRh-1O#I/74-1Fs5—.>:HNDO#2NPO 5DO#Tv.>=#-uI/NPO#QP74R#-1O#I/-(74-1FH58.>:GNPO#2NPO‡£ .>=58.;I/NPO].65D:GOvŠD-17 ^
kh^ Õ –—”´1
˜ 2K:GO#QX.K=#-Se#7K24.(:H24NPCSNP7Kd#=h:H2KCÓ.>=#-/NP7K-/CXf-1p„R#:<rD58FH-1O].ArP-/7K2K:GNPO#2AIJ5DOÄacQP:<rP-/O²@xNP7t.K=#-zO5—.>R#7K5DFnCE5Dd#2 , ºx9;=#-/7K- ¼ NP7b£ £.,8Á²º•9;=#-174Á Í $NPOºB£ ¼K¼ ^
kh^3Ö –—”´1˜ ÌNP7;QP7KNPRhd#21fNPO#-uI15DOÂ5DFG2KN¯2>5JŒ?.K=58.;.>=#-/7K-A:H2‹5¯NPO#-‰µ.>N8µ NPO#-wI/NP7K74-12Kd™NPOUµ
T#-/O#I1-ua™-/.´9-1-/O ¢D¡•¡ 2KRha#QP7KNDR#d#2;ND@ ))f#O#ND7KCE5DFcND7O#ND.1f5DO#T?.>=hNP2K-w24R#a#QP74NPR#d#2;ND@ .K=58.;I1NDO„.>5D:HOvŠ8-17 ^MÌNP7;5DFHQD-1a#7K5D2i:HOvQP-/O#-17K5DFfh.K=#:H2ia™-1I/NPCS-12‹5o24.65—.>-1CS-1O].t5Da™NPRh.
24R#a5DFGQP-1a#7K5D2;7>58.K=#-17.K=5DOX5Da™NPRh.;I1NDO#QP7KRh-1O#I/-(74-1Fs5—.>:HNDO#21^
\%h\ " % v ! #" $%
Rhd#dcND2K-ÈÁ8©‰ª6Á Í $NPO\ºB£ ¼ ^*,\-‰. ·©ÄLb£ .
£ ,DÁ8©E5DOhT (ƒLt£ £.,DÁ?ac-
.K=#-EO#58.>R#7K5DF‚=#NPCSNPCSNP7Kdh=#:H24CE2/^.$NPCza#:GO#:HO#Q?.K=#-124-Dfn9-YQD-/.(5X5v=#NPCSNPCSNP7Kdh=#:H24C
·© ((L£1 £.,DÁ8© ±£.,DÁ SºxO#ND.Oh-1I1-/2K2K5D7K:GFGŒXNPO].>N ¼ ^ =58.w:G2b:<.>2bŠ8-174O#-1F Œ
I/NPO#2K:GT#-174:HO#Q‹9;=#-1O { ª { ~ Í ¥ƒ=5JrP--/p„R5DFh:GCY58QP-12/f—9-$24-1-$.K=58..>=#-ŠD-174O#-1Fh:H2nÁ8© ‹Á ­^
Ì7KNDC .>=h:H2;5DO#Tv.>=h-ue#7K24.‹:G2KNPCSNP7Kdh=#:H24C .K=#-1NP74-1C 9-AQP-/.i.K=#:H2i@B5DI‰.JL
^ Ž ½ 6–—ž>‰¾ ,º "! !- -/%#!-$" !%'& *+.- #(-/% ¼ ^¶ÌNP7Y5DO 5DFGQP-1a#7K5)£ 5DOhT
Á8©‰ª6Á Í $NPOºB£ ¼ fP.K=#-174-i:H2M5O5—.>R#7K5DF#-1C°ac-/T#T#:HOhQAN8@c£.,hº¦Á8©(wÁ ¼) £.,DÁ8©
u£.,DÁ­^
º/Å R#a™T#:H74-1I‰.>ÆvCE-15DO#2.K=58.w.>=h-S:GCY58QP-zND@M.>=h-S-/Cza™-1T#T#:GO#Qv:HO#24:HT#-z.K=#-¯d#7KNqT#R#I‰.u:H2
FH5D7KQP-b-1O#NPRhQP=‡.KN¯CY5DdvNPO].KNE-15DI6=‡@B58I/.>ND71^‚mi=#:G2;9;:GFHFcac-u:HCSd™NP74.>5DO].iFs58.K-17/^ ¼
^ Õ –—ž6–—¡•¡<¢Dž…¿D˜ Ò @£ =5D2EI1NPOhQP7KR#-/O#I1-X7K-/Fs58.K:HNPO#2SÁ8©‰ª6ÁS9;:G.K= 8Á ©* ÁÂj ˆ º•.>=#-/pqR#5DFH:<.´ŒW7K-/Fs58.K:HNPO ¼ fU.K=#-1O‡£ ) £.,DÁ8©+£.,DÁ°º¦5DOv-/Czac-/T#T#:GO#Q ¼ ^
! #" % ! q" \%
, )
- ^ Ž/. ! !)0,-/ÌNP7;Á Í $NPOºB¥ ¼ L
Ú ×
ºŽ
º¦Õ
ºBÖ
ºx×
¼$Ò @
¼$Ò @
¼$Ò @
¼$Ò @
{z| } ºBCSNqTXÁ ¼ f#.K=#-1O { }|¶{X} ºBCSNUTXÁ ¼ ^
{ } 5DO#T {o|¶} ºBCSNqT²Á ¼ f#.>=h-1O M|¶{o|¶} ºxCENqT‡Á ¼ ^
{ };|¶{ ºBCSNUT‡Á ¼ f#.>=#-/O }|¶{X} ºBCSNUTXÁ ¼ f5DO#TvT#R58FHFGŒD^
{z| } ºBCSNqTXÁ ¼ 5DOhT }i
| ºBCSNUTXÁ ¼ fh.>=h-1O {°|
ºBCSNqTXÁ ¼ ^
- ^ Õ +.- #&*-/% º š ¼ š O#NPO#-/CEdh.´ŒX7K-/Fs58.K:HNPOXÁYNPOÂ5WFs58.4.>:HI/-(:G25YI/NPO#QP74R#-1OhI1-o7K-/Fs58.K:HNPO‡:G@58O#TÂNPO#F<Œ
:<@Áo2K58.>:G24e-/2°º Ž ¼ .>=h7KNPR#QD=ºx× ¼ ^
º ¼ ÌNP7z-1FG-1CS-1O].>2 { ª } ND@b5ÈFH58.K.K:HI/-ifI/NPO\º { ª }…¼ f.K=#-?2KCE5DFGFH-12`.oI1NDO#QP7KRh-1O#I/74-1Fs5—.>:HNDO±NPOÔ.K=58.A:HTh-1O].>:<e-12 { 5DOhT } fIJ5DOÄac-¯I1NDO#24.K7KR#I‰.>-1T)a„ŒÇ58d#d#FGŒq:GO#Qĺ Ž ¼
ºxR#O#FH-/2K2 { } 5DFG7K-J58ThŒ ¼ f8.K=#-1OWºÕ ¼ 5DO#TWº¦Ö ¼ 7K-/dc-158.>-/T#FGŒDfP5DOhT°.>=#-/OvºB× ¼ 74-1d™-J58.K-1T#F<ŒP^
mi=#:G2;:H2.>=h- ž…“•’ ›‰“ ¢D¡ I1NDO#QP7KRh-1O#I/-(74-1Fs5—.>:HNDO?I1NPO\º { ª }‰¼ ºxFHNy9-17`µ IJ5D24-uI ¼ ^
ÌNP7-h5DCEdhFH-12.KNo.>74ŒDf2K-/-(Ìn:HQPR#74-wÖh^$NPOhQP7KR#-/O#I1-A7K-/Fs58.K:HNPOh2IJ5DOva™-w:HO#Th:HIJ5—.>-1Tva]Œ
T587KŠD-/O#:HOhQE-15DI6=XI/NyrP-174:HO#QSa™-/.´9-1-1OX.´9$NS-1FG-1CS-1O].>2;:HO?.K=#-u2>5DCS-wa#FHNqI6Š^
ºx: ¼
}
{
{
ºB:G: ¼
}
}
ºB:H:G: ¼
}
{
ºB:<r ¼
{
}
}
{
{ j }
{
}
{
Ì:HQDR#7K-wÖUL NPCE-wFH58.K.K:HI/-12$@xNP79;=h:HI6=v.>N¯eO#T‡I1NPO#QD7KR#-/O#I1-AFs58.4.>:GI1-12
w!` Ñ %
. *#
!0- % "M! -174:G@•Œo.>=#58.5DO]ŒEI/NPO#QP74R#-1OhI1-b74-1FH58.>:GNPO¯NPOW5uQP7KNDR#dY:G224:HCSd#FGŒ(.>=#I/NP2K-‰.tTh-1I1NDCEd™NP2K:<.>:GNPO?T#-/.K-174CE:GO#-1Tva]Œv2KNPCS-wO#NP74CY58F·2KR#ahQP7KNPRhd·^
Ú Ù
. *#
!0- % ! #ÌNP7\QP-1Oh-17>58Fh5DFGQP-1ah7>5D2/f8d#74NyrP-wºB5 ¼ .>=#-Me7K2`.:G2KNPCSNP74d#=#:H24CÔ.>=h-1NP74-1C
ºxmi=#-1NP74-1C UÙ ^ Ž ¼ §\ºBa ¼ .K=#-uI1NP747K-/2Kd™NPO#T#-/O#I1-A.>=#-/NP7K-/C ºBmi=#-/NP7K-/C hk ^ Ž ¼ ^
. *#
!0- % iº¦5 ¼ š O]ŒW@xR#O#I‰.>:HNDO¨ÂL NPOv2K-‰.>2‹:HO#ThR#I1-/2b5DOv-/pqRh:Gr85DFH-/O#I174-1Fs5—.>:HNDOXNPOX:G.K2tT#NDCY5D:GOfc9;=#-/7K- ~ CE-15DO#2w¨º ¼ j*¨º ~ ¼ ^ =#Ny9 .>=58.‹@xNP7
QP74NPR#d#2 5DO#T))f:G@ L ) :G2(5‡=#NPCSNPCSNP7Kd#=h:H2KC .>=#-/O5DO]ŒÈ24:HO#QPFG-¯a#FHNqI6Š
[email protected]=#--/pqRh:Gr85DFH-/O#I1-b7K-1FH58.>:GNPOY:<.$:GO#T#R#I/-12iT#-‰.>-/7KCS:HO#-/2i5DFHF.K=#-a#FGNUI6Š„21^‹ºxmi=#:H2$:H29;=]Œ
.K=#-XÅ4ŠD-/7KO#-/FHÆSND@ :G2iT#-/eOh-1TX.KN¯ac-A5o2K:GO#QPFH-wahFHNqI6Š™f#.K=#-uNPO#-wI/NPO].65D:GO#:HO#QP^ ¼
ºxa ¼ :GrP-b5DO?- h5DCSd#FG-bND@\.´9N¯5DFHQP-/a#7>582i5DO#TW.´9No=#NPCSNPCSNP7Kd#=h:H2KCS2 ª ~ a™-/.´9-1-/O
.K=#-1C 24R#I6= .>=58. 5DOhT ~ QD:GrP-?Th: c-17K-/O].E-/p„R#:Gr85DFG-1O#I/-?7K-1FH58.>:GNPO#2°.K=58.¯T#NÈ=5JrD58.FH-J5824.wNPOh-oa#FHNqI6ŠX:GO±I1NPCSCSNPO·^EºBmi=#:G2:H2t9;=„Œ².>=#-ÇÅ4Š8-174O#-1FGƇN8@ :G2T#-‰eO#-1TÈ.>N
a™-A.K=#-(9;=hNPFH-A-1p„R#:<rD58FH-1OhI1-A7K-1FH58.>:GNPO‡7>58.K=#-17;.>=58OÂ5E24:HO#QDFH-ua#FHNqI6Šf™@xND7b5DFGQP-1ah7>5D2;:HO
QP-/O#-17K5DF^ ¼
. *#
!0- % Ud#Fs58:HOÇ=#Ny9 .>=#-SI1NPOhQP7KR#-/O#I1-EFs58.4.>:GI1-oND@$£ :H2(5v2KR#a#FH58.K.K:HI/-SN8@
.K=#-ud5D74.K:G.K:HNPOWFH58.K.K:HI/-ND@n¥ 582t5o24-/.J^
. *#
!0- % .658.K-È5DO#T d#7KNyrD-Ä5)rD-1742K:HNDOlND@Ami=#-/NP7K-/C ^ Ž .>=58.W7K-/@x-/7K2?.>N
.´9NÂ2KRh74 -1I‰.>:<rP-Y=hNPCENDCENP74d#=#:G2KCS2 ³bL\£ ³uºj Ž ª6Õ ¼ f7>58.K=#-17u.>=#5DOÄ.KNX.´9N
I/NPO#QP74R#-1O#I/-(74-1FH58.>:GNPO#2NPOv£?^
. *#
!0- % Ò @
L £ :G2W5)24R#74-/I/.K:GrP-²=#NPCSNPCEND7Kd#=#:G2KC‡f$24=#Ny9 .K=58.
‹
.K=#-174-E:G2u5‡FH58.K.K:HI1-o-/Cza™-1T#T#:GO#QvND@$NDOº ¼ :GO„.KN $NPOºB£ ¼ f\9;:<.>=±.>=h-E:GCY5DQD-zac-/:HO#Q
5DOv:GO„.K-17`rD58F^
. *#
!0- % Ò O]rP-1O].S5²I/NP7K74-124dcNPOhT#-1O#I/-Y.>=h-1NP74-1C ºBFH:GŠD-Smi=#-1ND7K-1Ckh^ Ž ¼ @xNP7°5
24R#74 -/I/.>:<rP-‹=#NPCSNPCSNP7Kd#=h:H2KC
L]£ ƒ.K=58.M74-1Fs5—.>-12M24R#a5DFGQP-1a#7K5D2MND@ [.KN(I/-174.>5D:HO
24R#a5DFGQP-1a#7K5D2;ND@n£?^ NPCS-1=#Ny9lT#-124I17K:Gac-u9;=#:GI6=XNPOh-121^tºtN¯d#7KNqND@n:H2i74-1p„R#:H74-1T·^ ¼
. *#
!0- % =hN­9l.>=5—.i.>=#-u2KRhacT#:G7K-/I/.‹-1Cza™-1ThT#:HO#Qo.K=#-1NP74-1C º ^ Ž ¼ =#NPFGT#2@xNP7
.K=#-u:HO].>-/7K2K-/I/.K:HNPOvND@5Sd™NP242K:HahFGŒW:GOheO#:<.>-b@B58CE:GFGŒSND@nI1NPO#QD7KR#-/O#I1-A7K-/Fs58.K:HNPO#2/^
. *#
!0- % ·ÌNP7.K=#-;IJ5D24-t£œj Zif].K=#-;7K:HOhQAN8@ :GO„.K-1QP-/7K2/fqQD:GrP-(ºB5 ¼ 5DOS- h5DCSd#FH-
ND@.>=h-o2KR#a™T#:H74-1I‰.(-/Cza™-1T#T#:GO#Q?.>=#-/NP7K-/CÃ:HO±9;=#:GI6=±.>=#-o.´9NXI/NPO#QP74R#-1O#I/-E74-1FH58.>:GNPO#2
I/NPCE-?@x74NPC d#74:HCS-‡:GT#-J58FH21f5DO#T¶ºBa ¼ 5DO- h5DCSd#FH-?9;=#-/7K-‡O#-1:<.>=#-/7EI/NPCS-12¯@x7KNPC 5
d#74:HCS-:HTh-J5DF¦^ Ò OX-15DI6=²I15D2K-8f2>5JŒ?9;=58.;.K=#-u-1Cza™-1T#Th:HO#Q¯T#Nq-12i.>N¯-15DI6=X-/FH-/CE-/O„.1^
. *#
!0- % M74NyrP-b.K=58.M.>=#-‹I1NDO#QP7KRh-1O#I/-Fs58.4.>:GI1-iND@·5AI6=58:HOYN8@·FH-/O#QD.K=YVĺ¦5D2
5DOX5DFGQP-1a#7K5¯9;:<.>=‡Fs58.4.>:GI1-wNPd™-17K58.>:GNPO#2 ¼ :G2;.K=#- $NUNDFH-J58O‡FH58.K.K:HI/-'! ¸ ^uºxmi=#- ¡H‰’qD” N8@
5oI6=5D:GOX:G2.>=#-uO„R#Cza™-17;ND@ 4 R#CSd#21fh2KNE5¯I6=#5D:HO‡ND@nFH-1OhQD.>=vVÈ=5D2;V € Ž -/FH-1CS-1O].K21^ ¼
Ú*k
. *#
!0- % w,-/. a™-?5ÂT#:G24.>74:Ha#RU.>:GrD-YFH58.K.K:HI1-Y5DO#T[I/NPO#2K:GT#-17z5DO]Œ Í ^
Ú-‰eO#-ÇCY5Ddh2²¨ L 5DO#TÔ¨
L a]Œl¨
8º ¼ j 5DOhT
¨—º ¼ j \^vºB5 ¼ =#Ny9œ.K=58.(¨°5DO#TĨ
z5D74-o=#NPCSNPCSNP7Kd#=h:H2KCS21^YºBa ¼ =#Ny9
.K=58..K=#-o:HO].>-/7K24-1I/.K:HNPOÈ[email protected]=#-1:G7wŠD-174O#-1FG2u:H2wˆÈºx:^g-D^<f-1p„R5DFG:G.´Œ ¼ ^YºBI ¼ 2K-¯mi=#-/NP7K-/CE2
¼ ^
^ Ž 5DO#T²ÙU^ Ž .KN¯2K=#Ny9¶.K=58. ) º'
. *#
!0- % ! $NPCSd#Rh.>-E5DFGF.>=#-Sd#7K:GO#I1:Gd5DF‚I/NPO#QP74R#-1O#I/-Y74-1Fs5—.>:HNDO#2u:HOÄÌ:HQPRh7KhÖ ^ Ò OhT#:HI158.>-ahFHNqI6Šq2ia]ŒYT5D7KŠ8-1O#:GO#QoI1NyrD-17K:GO#QP2;a™-/.´9-1-1Ov.´9NS-/FH-/CE-/O„.K2:HOW.K=#-w2>58CEa#FGNUI6Š^NPR‡CE5yŒYNPCS:G.i-#58CEd#FG-12;5DFG7K-15DThŒWThNPO#-u:HOvFH-/I/.KR#7K-8^
Ú