Agoh-Giuga conjecture

In 1950, Giuseppe Giuga conjectured that if and only if an integer p is prime then it will satisfy the congruenceMathworldPlanetmath


This is sometimes called the Giuga conjectureMathworldPlanetmath. Takashi Agoh rephrased the conjecture as pBp-1-1modp, where B is a Bernoulli numberMathworldPlanetmathPlanetmath; this is called the Agoh-Giuga conjecture. In 2003 Simon Plouffe performed an exhaustive search for a counterexample below 50000 but came up empty.

Title Agoh-Giuga conjecture
Canonical name AgohGiugaConjecture
Date of creation 2013-03-22 16:17:55
Last modified on 2013-03-22 16:17:55
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 11D85
Synonym Giuga conjecture
Synonym Giuga’s conjecture
Synonym Agoh conjecture
Synonym Agoh’s conjecture