Formula: Fermat's little Theorem

If $p \in {\mbox{${\mathbb{N}}$}}$ is a prime and $a \in {\mbox{${\mathbb{Z}}$}}$ then we have

$$a^p \ \equiv \ a \mod{\, p}$$ (4)

Moreover if $p$ does not divide $a$ then we have $a^{p-1} \ \equiv \ 1 \mod{\, p}$ .