Problem:
For how many real values of is an integer?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Suppose that is an integer. Then , and because is an integer, we have . Thus there are possible integer values of . For each such , the corresponding value of is . Because is positive and decreasing for , the values of are distinct.
The problems on this page are the property of the MAA's American Mathematics Competitions