Each of the n consecutive positive integers x+1, x+2, ...., x+n is expressible as the sum of squares of two distinct positive integers.

Determine the maximum value of n and prove that no higher value of n is possible.

I think the answer is 3.

What I'm having trouble proving is no two consecutive odd numbers are the sum of two distinct positive integers.

Posted by Jer on 2012-11-08 16:35:18