Fermat's Little Theorem/Proof 3

Proof
From the corollary to Reduced Residue System under Multiplication forms Abelian Group, the group of units of the ring $\Z / p \Z$ forms a group of order $p - 1$ under multiplication.

Because $p \nmid n$, the residue class of $n$ is invertible modulo $p$ and thus an element of this group.

By Order of Element Divides Order of Finite Group, we have:
 * $n^{p - 1} \equiv 1 \pmod p$