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In number theory the Agoh-Giuga conjecture on the Bernoulli numbers Bk postulates that p is a prime number if and only if
- Failed to parse (Missing texvc executable; please see math/README to configure.): 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 iff
- Failed to parse (Missing texvc executable; please see math/README to configure.): 1^{p-1}+2^{p-1}+ \cdots +(p-1)^{p-1} \equiv -1 \pmod p.
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).
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