Problem:
How many ordered pairs of positive integers, with , have the property that their squares differ by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and be, respectively, the larger and smaller of the integers. Then . Because is even, and are both even or are both odd. In either case and are both even. Hence there are four possibilities for , which are , and . The four corresponding values of are , and .
The problems on this page are the property of the MAA's American Mathematics Competitions