Agoh-Giuga conjecture

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

$pB_{p-1} \equiv -1 \pmod p.$

The conjecture as stated is due to Takashi Agoh (1990); an equivalent formulation is due to Giuseppe Giuga, from 1950, to the effect that p is prime if and only if

$1^{p-1}+2^{p-1}+ \cdots +(p-1)^{p-1} \equiv -1 \pmod p.$

[edit] References

Agoh, T, "On Giuga’s conjecture" Manuscripta Math., 87(4), 501–510 (1995).
Borwein, D.; Borwein, J. M., Borwein, P. B., and Girgensohn, R. "Giuga's Conjecture on Primality", American Mathematical Monthly, 103, 40-50, (1996). pdf
Giuga, G. "Su una presumibile proprietà caratteristica dei numeri primi", Ist. Lombardo Sci. Lett. Rend. A, 83, 511–528 (1950).