MathNet 2018-part-05 — 181 problems (EN–VI) Question 37

Prove that if $n \in \mathbb{N}^*$ and there exists $a, b \in \mathbb{Z}$ so that $\frac{a+bi}{\sqrt{n}}$ is a root of order $n$ of the unity, then $n = 8m^2$, for some integer $m$.