Pairwise distinct prime numbers $p, q, r$ satisfy the equality $$rp^3 + p^2 + p = 2rq^2 +q^2 + q.$$Determine all possible values of the product $pqr$.
Source: 2014 Belarusian MO A 11.2
Tags: number theory, diophantine, Diophantine equation
Pairwise distinct prime numbers $p, q, r$ satisfy the equality $$rp^3 + p^2 + p = 2rq^2 +q^2 + q.$$Determine all possible values of the product $pqr$.