Let G denote a group and let g ∈ G of finite order. Let k ∈ Z. Prove that there exists a unique integer r with 0 ≤ r < |g| such that $g^k =g^r$
I know since G is of finite order we know that the order of $g^n$=e for some positive n
I'm a little stuck on how to begin or where to go from here, any direction would be great.