I want to show that $\displaystyle x^2-10y^2 = \pm 2$ is insoluble in integers. I've tried factorisation in $\displaystyle \mathbb{Z}[\sqrt{10}]$ but this isn't a UFD so I can't get things to work. I've also tried considering norms. Is there a more elementary idea that can show this? I assume we should look for a contradiction. By simple "odd/even" arguments it's clear that $\displaystyle x$ must be even and $\displaystyle y$ must be odd, but I can't get much further. If anyone's able to give a hint then that would be most appreciated!

EDIT: OK I've spotted it - just look at the equation modulo 10 ! Incidentally, is there a way of deleting a question of yours so that other people won't waste time trying to answer something you've already done?