The RSA encryption scheme is based on it, and generalizations of it include the defintion of the Carmichael function and one that uses the totient function.
A generalization of this theorem to polynomials is the basis for the Agrawal-Kayal-Saxena algorithm, and this theorem can be used to prove that the periodicity of the decimal representation of a prime-denominator fraction is some multiple of p-1. A combinatorial proof of it considers a bracelet with a string of symbols, while its more easily proven via group theory using Lagrange's theorem. The RSA encryption scheme is based on it, and generalizations of it include the defintion of the Carmichael function and one that uses the totient function. For 10 points, name this theorem that states a to the p is congruent to a mod p, for p prime.
A generalization of this theorem to polynomials is the basis for the Agrawal-Kayal-Saxena algorithm, and this theorem can be used to prove that the periodicity of the decimal representation of a prime-denominator fraction is some multiple of p-1.
{Fermat's little} theorem