Let $G$ be a group and $a$ an element of $G$ of order $n$.
Prove that: If $a^k = e$, then $n$ divides $k$
Let $G$ be a group and $a$ an element of $G$ of order $n$.
Prove that: If $a^k = e$, then $n$ divides $k$
Here's a hint: Try writing $k=qn+r$ with $0\leq r
If $r\neq 0$, can you find a contradiction?