RO-NMO 2017 Problem 123

Let $G$ be a finite group with the following property:

If $f$ is an automorphism of $G$ , then there exists $m\in\mathbb{N^\star}$ , so that $f(x)=x^{m}$ for all $x\in G$ .

Prove that G is commutative.

Marian Andronache