How can you show that if $a, m,$ and $n$ are positive integers with $a>1$ and $(a^m + 1)$ divides $(a^n + 1)$ then $m$ divides $n?$
I tried using modular arithmetic but I couldn't move further please help
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2Quick beginner guide for asking a well-received question + please avoid "no clue" questions – Anne Bauval Jun 13 '23 at 09:08
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4Does this answer your question? If $a^{m}+1\mid a^{n}+1$ then prove that $m\mid n$. (First hit on Approach$0$) – Anne Bauval Jun 13 '23 at 09:20