Determine the prime numbers $p$ and $q$ that satisfy the equality: $p^3 + 107 = 2q (17q + 24)$ .
Source: 2014 Romania JBMO TST 3.2
Tags: number theory, Diophantine equation, diophantine
Determine the prime numbers $p$ and $q$ that satisfy the equality: $p^3 + 107 = 2q (17q + 24)$ .