$a,b,r,s$ are coprime such that $a^2+b^2=r^2$ and $a^2-b^2=s^2$. I’m trying to show that $a, r, s$ is odd and $b$ is even.
If we add the equations, we get $2a^2=r^2+s^2$. Hence $r^2 + s^2$ is even. The square of number is even/odd iff the number is even/odd. Either $r^2$ and $s^2$ are both even or both odd since their sum is even. Thus $r$ and $s$ are both odd since they are coprime.
I’m only able to show that either $a$ is even and $b$ is odd or $a$ is odd and $b$ is even. Any hints are appreciated. Thanks