Show that if n is the sum of two squares, then it CAN"T be congruent to 3 mod 4.

Proof:

Let n = x^2 + y^2

Assume, aiming for a contradiction, that n is congruent to 3 mod 4.

So, x^2 + y^2 is congruent to 3 mod 4

This implies that 4 | x^2 + y^2 -3

I'm trying to get a contradiction, but I'm stuck here...

Any advice... Thanks..