A remark on the Chebotarev theorem about roots of unity

Abstract

Let $\Omega$ be a matrix with entries $a_{i,j}={\omega }^{ij},$ $1\le i,j\le n,$ where $\omega =e^{2\pi \sqrt{-1}/n},$ $n\in \mathbb{N}.$ The Chebotarev theorem states that if $n$ is a prime then any minor of $\Omega$ is non-zero. In this note we provide an analogue of this statement for composite $n.$