Generalizations of Fermat's Little Theorem via Group Theory

Abstract

Let p be a prime number and a be an integer. Fermat’s little theorem states that a ≡ a (mod p). This result is generally established by an appeal to the theorem of elementary group theory that asserts that x|G| = 1 for every element x of a finite group G. In this note we describe another way that group theory can be used to establish Fermat’s little theorem and related results.