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Agoh-Giuga conjecture

In number theory the Agoh-Giuga conjecture on the Bernoulli numbers Bk postulates that p is a prime number if and only if

pBp−1 is congruent to −1 mod p.

The conjecture as stated is due to Takashi Agoh ; an equivalent formulation is due to Giuseppe Giuga , from 1950, to the effect that p is prime if and only if

1^{p-1}+2^{p-1}+ \cdots +(p-1)^{p-1} \equiv -1 \pmod p.
01-04-2007 01:16:19
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