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## Homework Statement

If M and N are positive integers >2, prove that ((2^m)-1) is not a divisor of ((2^n)+1)

## Homework Equations

## The Attempt at a Solution

Is this correct? I use the well-ordering principle.

Let T be the set of all M,N positive integers greater than 2 such that ((2^m)-1)/((2^n)+1). Assume T is non-empty, then by the WOP, T must contain a smallest L element, call it((2^k)-1)/((2^L)+1). but (2^(k+1)-1)/(2^(L+1)+1) is in T. So, ((2^k)*(2^1)-1)/((2^L)*(2^1)+1). Thus, I have a contradiction.