Euler's theorem

Generalizes Fermat’s little theorem.

Theorem 1(Theorem).

If $a$ and $n$ are co-prime, then $a^{\varphi (n)}\equiv 1\mathrm{mod}n$.

where $\varphi (n)$ is the Euler totient function, which counts the number of integers less than or equal to  n  that are co-prime to  n.

Proof every similar to that of Fermat’s little theorem.