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..