Problem

Source: 2016 Saudi Arabia IMO TST , level 4+, I p1

Tags: number theory, Sum, coprime



Call a positive integer $N \ge 2$ special if for every k such that $2 \le k \le N, N$ can be expressed as a sum of $k$ positive integers that are relatively prime to $N$ (although not necessarily relatively prime to each other). Find all special positive integers.