Tuesday, December 1, 2015

elementary number theory - Show that $gcd(2^m-1, 2^n-1) = 2^ {gcd(m,n)} -1$




I'm trying to figure this out:


Show that for all positive integers $m$ and $n$


$\gcd(2^m-1, 2^n-1) = 2^{\gcd(m,n)} -1$



I appreciate your help, Thanks.


Note: $\gcd$ stands for the greatest common divisor.

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