prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$ 
Prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$.

Do I use the terms $x= r^2 - s^2$, $y = 2rs$, and $z = r^2 + s^2$ to prove this problem?
Thanks for any help.

Hint Let $w=z^2$. Then 
$$x^2+y^2=w^2$$
Solve this Pytagorean equation, and prove that infinitely many $w$ are perfect squares.
With your notation $w=r^2+s^2$ so you need $r,s$ to satisfy $r^2+s^2=z^2$...
