Fermat’s Theorem and Wilson’s Theorem

Abstract

Fermat’s Theorem states that, for every prime number p, if p does not divide the natural number a, then a to the power p − 1 leaves a remainder of 1 upon division by p. This beautiful theorem has a number of important theoretical and practical applications, one of which is to the technique for sending secret messages that is described in the following chapter. We present proofs of Fermat’s Theorem and also of Wilson’s Theorem, another beautiful formula in modular arithmetic.