$p, q, r$ are distinct prime numbers which satisfy $$2pqr + 50pq = 7pqr + 55pr = 8pqr + 12qr = A$$for natural number $A$. Find all values of $A$.
Source: Second Saudi Arabia JBMO TST 2018, P1
Tags: number theory
$p, q, r$ are distinct prime numbers which satisfy $$2pqr + 50pq = 7pqr + 55pr = 8pqr + 12qr = A$$for natural number $A$. Find all values of $A$.