(In reply to
Fixing the prior proof (spoiler) by Steve Herman)
Steve, I think my proof holds up although I could/should have been clearer.
A=2m+1, B=2n+1
A^2 + B^2 = 4m^2 + 4m + 1 + 4n^2 + 4n + 1 = 14C^2
2m^2 + 2m + 2n^2 + 2n + 1 = 7C^2
2m(m+1) + 2n(n+1) + 1 = 7C^2
Each of the first two terms is divisible by 4 since each is twice the product of consecutive integers.
However, overall I prefer your proof. It's shorter and more direct and avoids any odd/even byways.

Posted by xdog
on 20150507 20:09:23 