For which integers $n \ge 2$ can we arrange numbers $1,2, \ldots, n$ in a row, such that for all integers $1 \le k \le n$ the sum of the first $k$ numbers in the row is divisible by $k$?
Source: Switzerland Final Round 2021 P5
Tags: number theory
For which integers $n \ge 2$ can we arrange numbers $1,2, \ldots, n$ in a row, such that for all integers $1 \le k \le n$ the sum of the first $k$ numbers in the row is divisible by $k$?