Chebotaryov theorem on roots of unity

The theorem state that all submatrices of a DFT matrix of prime length are invertible.

The Chebotaryov theorem on roots of unity was originally a conjecture made by Ostrowski in the context of lacunary series. Chebotaryov was the first to prove it, in the 1930s. This proof involves tools from Galois theory and did not please Ostrowski, who made comments arguing that it "does not meet the requirements of mathematical esthetics" .

Several proofs have been proposed since, and it has even been discovered independently by Dieudonné.

Let ${\displaystyle \Omega }$ be a matrix with entries ${\displaystyle a_{ij}=\omega ^{ij},1\leq i,j\leq n}$, where ${\displaystyle \omega =e^{2i\pi /n},n\in \mathbb {N} }$. If ${\displaystyle n}$ is prime then any minor of ${\displaystyle \Omega }$ is non-zero.

...
Wikipedia