Challenge Level

The numbers 4 and 12 have a special property.

$$\begin{eqnarray} 4 + 12&= 16\\ 4 \times 12&= 48 \end{eqnarray}$$

and 16 is a factor of 48.

Find some other examples of pairs of numbers such that their sum is a factor of their product.

What condition must exist for pairs of numbers to be related in this way?