CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search For other theorems named after Pierre de Fermat, see Fermat's theorem . Fermat's little theorem states that if p is a prime number , then for any integer a , the number a p − 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, 2 7 = 128, and 128 − 2 = 7 × 18 is an integer multiple of 7. If a is not divisible by p , Fermat's little theorem is equivalent to the statement that a p − 1 − 1 is an integer multiple of p , or in symbols a p − − 1 ≡ ≡ 1 ( mod p ) . {\displaystyle a^{p-1}\equiv 1{\pmod {p}}.} [1] [2] For example, if a = 2 and p = 7 then 2 6 = 64 and 64 − 1 = 63 is thus a multiple of 7....