Problem:
For how many positive integer values of is the expression an integer?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since is a positive integer, must be a positive integer divisor of . There are positive integer divisors of :
Express these numbers in the form :
Of these, seven have a positive value for .
Given , it follows that . Since must be a divisor of , there are such divisors greater than .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions