Proving $n$ divides $φ(a^n − 1)$ for any positive integer $a$ and $n$, where $a^n - 1 > 1$

Question

How will I be able to show that $n|φ(a^n − 1)$ for any positive integer $a$ and $n$, where $a^n - 1 >1$? I already have an idea that I will probably need to use cyclotomic polynomials. Will I also need to use the fact that $o_{an−1}(a) = n$?

Thank you!