If $k$ is the smallest positive integer such that $a^k=1$ and $a^n=1$, where $a$ is an element of group $G$, $n\in\mathbb{Z^+}$, then $k$ divides $n$
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.