Show that if m does not = n then
gcd((a^2)^n) + 1, ((a^2)^m + 1) = 1, if a is even
and 2, if a is odd.
Theorem: WLOG, for
Proof: Start by noticing -- see proof at http://www.mathhelpforum.com/math-he...s-2-n-1-a.html. So we can rewrite as , for and some x. It can be easily seen that k has the opposite parity of a. So if a is even, k is odd, and . If a is odd, k is even, and . QED