Fermat's little theorem

A prime p divides a^p–a for any integer a

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as a p ≡ a ( mod p) . {\displaystyle a^{p}\equiv a{\pmod {p}}.} For example, if a = 2 and p = 7, then 27 = 128, and 128 − 2 = 126 = 7 × 18 is an integer multiple of 7.

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