MathNet 2019-part-01 — 184 problems (EN–VI) Question 102

A chessboard has the form of an $n \times n$ torus, where $n = 2^{2k} + 1$. Prove that $n$ queens in the cells $(i, 2^k \cdot i)$ ($1 \le i \le n$, multiplication modulo $n$) do not attack each other.