Fermat's Little Theorem/Proof 3

Proof
Let $\struct {\Z'_p, \times}$ denote the multiplicative group of reduced residues modulo $p$.

From the corollary to Reduced Residue System under Multiplication forms Abelian Group, $\struct {\Z'_p, \times}$ forms a group of order $p - 1$ under modulo multiplication.

By Element to Power of Group Order is Identity, we have:
 * $n^{p - 1} \equiv 1 \pmod p$