Find all pairs of positive integers $m$ and $n$ such that $$(m + 1)! + (n + 1)! = m^2n.$$
Problem
Source: New Zealand NZMOC Camp Selection Problems 2011 Juniors 4
Tags: diophantine, Diophantine equation, number theory
Source: New Zealand NZMOC Camp Selection Problems 2011 Juniors 4
Tags: diophantine, Diophantine equation, number theory
Find all pairs of positive integers $m$ and $n$ such that $$(m + 1)! + (n + 1)! = m^2n.$$