Fermat’s Little Theorem

If $p ∈ P$ is a prime number and $k ∈ Z$ is an integer, then the following holds:

$$k^p ≡ k \mod p$$

If $k$ is coprime to $p$, then we can divide both sides of this congruence by $k$ and rewrite the expression into the following equivalent form:

$$k^{p−1} ≡ 1 \mod p$$

Fermat's little theorem is a special case of Euler's theorem.