discrete mathematics - Proof: For all integers $x$ and $y$, if $x^2+ y^2= 0$ then $x =0$ and $y =0$

I need help proving the following statement:

For all integers $x$ and $y$, if $x^2+ y^2= 0$ then $x =0$ and $y =0$

The statement is true, I just need to know the thought process, or a lead in the right direction. I think I might have to use a contradiction, but I don't know where to begin.

Any help would be much appreciated.

Answer

If $x\ne 0$ or $y\ne 0$ then $|x| \ge 1$ or $|y| \ge 1$, which implies $x^2+y^2 \ge 1$.