Find all positive integer triples $(x, y, z)$ such that $1 + 2^x \cdot 3^y=5^z$ is true.
Problem
Source: : China Northern MO 2010 p3 CNMO
Tags: number theory, Diophantine equation, diophantine
Source: : China Northern MO 2010 p3 CNMO
Tags: number theory, Diophantine equation, diophantine
Find all positive integer triples $(x, y, z)$ such that $1 + 2^x \cdot 3^y=5^z$ is true.