abstract algebra - Power of an $r$-cycle is an $r$-cycle
I'm trying to prove that if $\alpha$ is an $r$-cycle in $S_n$ then $\alpha^k$ is an $r$-cycle if and only if $(k,r)=1$, but I'm having trouble proving that if $(k,r)=1$ then $\alpha^k$ is an $r$-cycle.
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