Problem:
Find the number of ordered pairs of positive integers such that .
Solution:
We start by finding the number of perfect square factors of .
Factoring, . So, has perfect square factors. As is positive, each such factor corresponds to one value of . Once we have a value of , the value of is fixed at . So, our answer is the number of perfect square factors of , which is .
The problems on this page are the property of the MAA's American Mathematics Competitions