A remark on the Chebotarev theorem about roots of unity

Abstract

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