Number Theory calculation problem

Question

I was working through a set of lecture notes, and I saw the following line:

$u^2+5v^2 = \pm 1$ or $\pm2$, and so it follows that $v=0$.

I can't see how this line is clear, and can't see how to do this without quite a lot of effort. If someone could provide an easy explanation, that would appreciated.

Answer 1

If $v\ne 0 $ then $u^2+5v^2 \ge 0+5= 5$