# Fermat's Little 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 $$p$$,

$a^p \equiv a \pmod{p}\,.$

When $$\gcd(a, p) = 1$$, then,

$a^{p-1} \equiv 1 \pmod{p} \,.$