Problem

Source: 2012 Indonesia Round 2.5 TST 1 Problem 4

Tags: number theory, greatest common divisor, modular arithmetic, number theory proposed



Determine all integer $n > 1$ such that \[\gcd \left( n, \dfrac{n-m}{\gcd(n,m)} \right) = 1\] for all integer $1 \le m < n$.