8. A broken calculator has the + and $\times$ keys switched. For how many ordered pairs $(a, b)$ of integers will it correctly calculate $a+b$ using the labelled + key?
Solution: $\square$
We need $a+b=a b$, or $a=\frac{b}{b-1}=1-\frac{1}{b-1}$, so $1 /(b-1)$ is an integer. Thus $b$ must be 0 or 2 , and $a$ is 0 or 2 , respectively. So there are 2 .