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elementary number theory - Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$ - Mathematics Stack Exchange
https://math.stackexchange.com/questions/7473/prove-that-gcdan-1-am-1-a-gcdn-m-1
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induction
ideals
divisibility
elementary-number-theory
gcd-and-lcm
For all $a, m, n \in \mathbb{Z}^+$, $$\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$$
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