Let $m$ and $n$ be two positive integers such that $m+n+mn=118.$
My question is: Can the value of $(m+n)$ be uniquely determined?
I find by inspection that the pair $(m,n)=(16,6)$ (or the pair $(6,16)$) satisfies the above equation, i.e. $m+n=22$ satisfies the above equation. I guess that the value of $(m+n)$ can't be uniquely determined, but I neither find any other values of $m+n$. Any hints/way to tackle this problem?