1. 3^M+4^M is odd, so even M merit no further consideration.
2. By reason of addition/multiplication of powers, we need further only check odd prime M.
3. If M is odd prime, then we have 3^(M1) congruent to 1 and 4^(M1) congruent to 1, modM (Fermat).
4. Hence, 3^M is worth 3, mod5 or larger and 4^M is worth 4, mod5 or larger.
5. Accordingly, M is always divisible by 7.
Edited on November 13, 2010, 12:40 pm

Posted by broll
on 20101113 12:39:18 