Fermat's Little TheoremFermat's little theorem states that for an integer, n, and a prime, p, that does not divide n, n^{p1} = 1 (mod p). For example, for p = 5, 2^{4} = 16 and 16 = 1 (mod 5) 3^{4} = 81 and 81 = 1 (mod 5) 4^{4} = 256 and 256 = 1 (mod 5) 6^{4} = 1296 and 1296 = 1 (mod 5) etc. See Fermat's Little Theorem and its links (especially its interactive modular arithmetic table) for an introduction and proof. Notation note: ap means that p divides a. For a more advanced discussion and additional proofs, see How to Discover the Statement and Two Proofs of Fermat's Little Theorem.

Translations of mathematical formulas for web display were created by tex4ht. 