All variables here are integers.
$$z^2=x^2+4y$$
I am trying to generate all $x,y$, given valid ranges $1\leq x\leq N$ and $-N\leq y\leq N$ intelligently.
Basically, given a selection of $x$ from 1 to $N$, I'd like to know the lower and upper integer bounds for $z$. Or, if it's easier, a selection of $y$ instead.