Problem

Source: INMO 2022 Problem 2

Tags: INMO, INMO 2022, combinatorics, algebra



Find all natural numbers $n$ for which there is a permutation $\sigma$ of $\{1,2,\ldots, n\}$ that satisfies: \[ \sum_{i=1}^n \sigma(i)(-2)^{i-1}=0 \]