How can I prove that the value of $\varphi(p^n-1)$ (where $p$ is prime and $n$ is some positive integer) is some multiple of $n$? The purpose of this is to prove that $n$ divides $\varphi(p^n-1)$.
2026-03-30 05:32:03.1774848723
If $p$ is prime, then $n\mid\varphi(p^n-1)$
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Consider the group of units $\Bbb Z/D\Bbb Z^\times$ where $D=p^n-1$, $p$ a prime.
What is the order of $p$?