This is based on a earlier post on this forum only. Following lemma was used to solve a problem posted earlier - http://www.mathhelpforum.com/math-he...rs-155363.html

$\displaystyle (m,n) =1 \implies (2^m-1,2^n-1) = 1$

My question how do I prove this?

I have made an attempt but am stuck at this -

Given- Let m,n be any +ve integers. If a proposition is true for m and n then following holds true

1. proposition is true for (m+n)

2. proposition is true for (m-n), provided (m-n)>0

Claim- Proposition is true for all

am + bn, provided (am + bn) > 0, where a,b are any intergers (not necessarily >0)

How do I prove my claim? Some sort of induction?

Please help