For $\sigma=(1,2,\dots,n)\in S_n$, I need to show if $\tau\in S_n$ commutes with $\sigma$ then $\tau=\sigma^k$ for some $k\ge 1$.

Question

$\sigma=(1,2,\dots,n)\in S_n$, I need to show if $\tau\in S_n$ commutes with $\sigma$ then $\tau=\sigma^k$ for some $k\ge 1$

Thank you for help. I only knew only disjoint cycles commutes .