Find all pairs of prime numbers $p$ and $q$ that satisfy the equation $3p^{q}-2q^{p-1}=19$.
Problem
Source: Ukrainian National Math Olympiad 4th round
Tags: modular arithmetic, number theory unsolved, number theory
Source: Ukrainian National Math Olympiad 4th round
Tags: modular arithmetic, number theory unsolved, number theory
Find all pairs of prime numbers $p$ and $q$ that satisfy the equation $3p^{q}-2q^{p-1}=19$.