Very nice! Another easy one is looking at it modulo 4. The powers on the left-hand side are both odd perfect squares, which are thus 1 modulo 4. So their sum i

Very nice! Another easy one is looking at it modulo 4. The powers on the left-hand side are both odd perfect squares, which are thus 1 modulo 4. So their sum is 2 modulo 4. But the right-hand side is an even perfect square, which is 0 modulo 4. EDIT. I guess my modulo-100 discussion is really just a convoluted way of coming up with the above fact.