Saturday, December 16, 2017

elementary number theory - Does $3$ divide $2^{2n}-1$?

Prove or find a counter example of : $3$ divide $2^{2n}-1$ for all $n\in\mathbb N$.


I compute $2^{2n}-1$ until $n=5$ and it looks to work, but how can I prove this ? I tried by contradiction, but impossible to conclude. Any idea ?

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