Suppose that $a$ and $b$ are positive integers such that $ab$ divides $a + b$.
Prove that $a = b$, then prove that $a$ is either $1$ or $2$.
I was thinking using the theorem:
If $n|a$ and $n|b$,then $n|(ax+by)$ for any $x,y\in \mathbb Z$.
Then I can derive that $ab$ divides $a$ and $b$. I could not go further. However, this doesn't seem like can help me solve the question I had.