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Proof that if m is odd then gcd(5,2^m-1)=1

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    $$2^{2m+1}-1 \equiv 2(-1)^m-1 \in \{1,2\}\pmod{5}$$ – 2017-02-27
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    Quelle est votre question exactement? – 2017-02-27
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    i need a proof of the => – 2017-02-27

1 Answers 1

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Hint :

$5$ is a prime number.

So, if a positive integer $d$ divides simultaneously $5$ and $2^n-1$ and if $d\neq 1$, then ...