MathNet 1994 — Part 01 Question 35

Show that every positive integral power of $\sqrt{2}-1$ is of the form $\sqrt{m}-\sqrt{m-1}$ for some positive integer $m$. (e.g. $\left.(\sqrt{2}-1)^{2}=3-2 \sqrt{2}=\sqrt{9}-\sqrt{8}\right)$.