# Thread: Proof about squares of odd numbers

1. ## Proof about squares of odd numbers

Hello community. I've been having a hard time proving this: The sum of the squares of odd integers cannot be a perfect square. I'd appreciate any direct help or hint

2. ## Re: Proof about squares of odd numbers

Prove first that the sum of two odd squares is 2 more than a multiple of 4.

This tells us that it is an even number, but not divisible by 4.

But if this summed to a square, that square being even, would have to be a square of another even number, and thus 4 would divide it.

3. ## Re: Proof about squares of odd numbers

Hehe was pretty straightforward. Thank you