Fermat's Little Theorem

Theorem
If $p$ is a prime number and $p \nmid n$, then $n^{p-1} \equiv 1 \pmod p$.

Also known as
Some sources call this Fermat's Theorem, but it needs to be appreciated that this may cause confusion with Fermat's Last Theorem.

It dates from 1640.

Some refer to the corollary $n^p \equiv n \pmod p$ as Fermat's little theorem and from it derive this result.