Agoh-Giuga conjecture∗
PrimeFan†
2013-03-21 21:16:59
In 1950, Giuseppe Giuga conjectured that if and only if an integer p is prime
then it will satisfy the congruence
p−1
X
ip−1 ≡ −1
mod p.
i=1
This is sometimes called the Giuga conjecture. Takashi Agoh rephrased the
conjecture as pBp−1 ≡ −1 mod p, where B is a Bernoulli number; this is called
the Agoh-Giuga conjecture. In 2003 Simon Plouffe performed an exhaustive
search for a counterexample below 50000 but came up empty.
∗ hAgohGiugaConjecturei created: h2013-03-21i by: hPrimeFani version: h38419i Privacy
setting: h1i hConjecturei h11D85i
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