How do i solve this problem? (Greatest common divisor) – math.stackexchange.com

How do i solve this problem? (Greatest common divisor) – math.stackexchange.com

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For each $n\in\mathbb{N}$ show that \begin{equation} \text{gcd}(3^{n}+5^{n+1},3^{n+1}+5^{n})=2\ \text{or}\ 14. \end{equation} I tried induction but i got stuck.

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