Problem:
For how many positive integers is also a positive integer?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let so that . Because and are relatively prime, it follows that must be a factor of 30 . Because is positive and less than 30 it follows that . Thus equals , or 30 . Hence there are possible values for , namely 15, 20, 24, 25, 27, 28, and 29.
The problems on this page are the property of the MAA's American Mathematics Competitions