Find all integers $c$ such that the equation $(2a+b) (2b+a) =5^c$ has integer solutions.
Problem
Source: Norwegian Mathematical Olympiad 2002 - Abel Competition p1b
Tags: diophantine, Diophantine equation, number theory
Source: Norwegian Mathematical Olympiad 2002 - Abel Competition p1b
Tags: diophantine, Diophantine equation, number theory
Find all integers $c$ such that the equation $(2a+b) (2b+a) =5^c$ has integer solutions.