Problem:
Positive integers and are such that the graphs of and intersect the -axis at the same point. What is the sum of all possible coordinates of these points of intersection?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Setting in both equations and solving for gives , so . Only four pairs of positive integers have product , namely , and . Therefore the four possible points on the -axis have coordinates , and , the sum of which is .
The problems on this page are the property of the MAA's American Mathematics Competitions