I have been stuck on this question for quite some time, I have tried several methods but to no avail. I attempted to use prime factorization but I couldn't really see where to go with it.
2026-04-01 08:02:51.1775030571
Prove that if $m\mid (a^2 -1)$ then $m\mid (a^4 -1)$
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$a^4-1=(a^2)^2-1^2=(a^2-1)(a^2+1) \Rightarrow (a^2-1)|(a^4-1).$
If $m|(a^2-1)\Rightarrow \exists n$ sunch that $a^2-1=mn\Rightarrow a^4-1=mn(a^2+1)\Rightarrow m|(a^4-1)$