Possible Duplicate:
$a^2-b^2 = x$ where $a,b,x$ are natural numbers
- Show that for every positive odd integer $x$ there exist integers $y$ and $z$ such that $(x, y, z)$ is a solution
- For which positive even integers $x$ do there exist integers $y$ and $z$ such that $(x, y, z)$ is a solution
I have thought about trying a solution through congruence modulo but I head nowhere.
Here is my work so far:
But I think maybe infinite descents would be more appropriate but just don't know how to do it.
