Show that $n$ divides $\phi(a^n -1)$

Asked Oct 06 '16 at 13:29

Active Oct 06 '16 at 13:29

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Show that $n$ divides $\phi(a^n -1)$ for any $a>n$ where $\phi$ is Euler's totient function.

I would really appreciate a hint.

asked Oct 06 '16 at 13:29

Emil

2

Hint: What is the order of $a$ modulo $a^n-1$? – Thomas Andrews Oct 06 '16 at 13:32
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Hint:Use Lagrange's theorem on groups. – Sai Teja Oct 06 '16 at 13:32
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See http://math.stackexchange.com/questions/930235/number-theoretic-proof-that-n-mid-phian-1?noredirect=1&lq=1 or http://math.stackexchange.com/questions/398165/n-divides-phian-1-where-a-n-are-positive-integer – Oct 06 '16 at 14:03

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