Find all triples $(x,y,z)$ of positive integers such that $3^x + 4^y = 5^z$.
Problem
Source: 2010 Saudi Arabia BMO TST 4.1 - Balkan Math Olympiad
Tags: diophantine, Diophantine equation, number theory
Source: 2010 Saudi Arabia BMO TST 4.1 - Balkan Math Olympiad
Tags: diophantine, Diophantine equation, number theory
Find all triples $(x,y,z)$ of positive integers such that $3^x + 4^y = 5^z$.