I would like a hint for the following Diophantine equation: $a^n-b^n=8$ with $a,b\in\mathbb{Z}$ and $n\in \mathbb{Z}_{\geq 2}$.
I know this can be done with estimates, but all my tries led nowhere. Help would be appreciated!
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Use https://math.stackexchange.com/questions/188657/why-is-an-bn-divisible-by-a-b – lab bhattacharjee Oct 31 '19 at 10:57
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2See this question – J.-E. Pin Oct 31 '19 at 10:57
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Thank you. I didn't know it was already asked. – MBéla Oct 31 '19 at 11:02
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$a-b$ is a factor only factors of 8 are 1,2,4,8 . – Oct 31 '19 at 12:28