Problem:
How many ordered pairs of integers satisfy ?
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
Notice that , and if is a solution, then so is . Assume . Squaring both sides of the given equation gives , so . Because and are positive integers, either , or and . The first case gives as a solution, and the second case gives as a solution. Because is squared in the given equation, the corresponding negative values for also give solutions: and . There are solutions in all.
The problems on this page are the property of the MAA's American Mathematics Competitions