Problem

Source: 2015 Taiwan TST Round 1 Quiz 1 Problem 1

Tags: number theory, Taiwan, Taiwan TST 2015, BritishMathematicalOlympiad



Find all primes $p,q,r$ such that $qr-1$ is divisible by $p$, $pr-1$ is divisible by $q$, $pq-1$ is divisible by $r$.