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Special Sums and Products

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?