Find all primes $p, q$ satisfying the equation $2p^q - q^p = 7.$
Problem
Source: 2010 Saudi Arabia BMO TST 5.4 - Balkan Math Olympiad
Tags: Diophantine equation, diophantine, number theory
Source: 2010 Saudi Arabia BMO TST 5.4 - Balkan Math Olympiad
Tags: Diophantine equation, diophantine, number theory
Find all primes $p, q$ satisfying the equation $2p^q - q^p = 7.$