# Sum of two squares proof. Help please.

• Sep 11th 2007, 01:41 PM
Milly1990
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. :confused:

"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..

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