XK-TST 2015 Problem 1

a)Prove that for every n,natural number exist natural numbers a and b such that $(1-\sqrt{2})^n=a-b\sqrt{2}$ and $a^2-2b^2=(-1)^n$ b)Using first equation prove that for every n exist m such that $(\sqrt{2}-1)^n=\sqrt{m}-\sqrt{m-1}$