# Math Help - Sum of two squares proof. Help please.

1. ## Sum of two squares proof. Help please.

Good evening,

I have this question for a mere tenth of my homework... and I'm a bit puzzled as to how to prove the theory... any help would be appreciated.

"For any pair of numbers, x and y, 2(x^2+y^2) is the sum of the two squares." Prove this statement.

I believe that the statement is true, and it is a proof by direct argument... however, my initial attempts at solving it algebraically failed miserably!

I understand that it must have something to do with one of Fermat's theories, something to do with "4k+1" and prime numbers... but as of yet I've never learned anything about it..

Thanks, Milly.

2. Did you consider $\left( {x + y} \right)^2 + \left( {x - y} \right)^2$?

3. ## Thank you!!!

No I didn't consider it!
I'm going to blame it on being back to school for two days after 6 weeks off!!
Haha, thanks very much!!

Milly.