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## Homework Statement

If a is an element of a group and |a|=n, prove that C(a)=C(a^k) when k is relatively prime to n.

## Homework Equations

If n and k are relatively prime, then there exists integers s and t such that ns+kt=1.

The centralizer a in G, C(a) is the set of all elements in a group G that commute with a. C(a)={g an element of G|ga-ag}

## The Attempt at a Solution

I tried proving it by double containment, but I couldn't show that C(a^K) is contained in C(a). Should I try a proof by contradiction? I will be grateful for any help.