Problem:
Let be a positive integer such that is an integer. Which of the following statements is not true:
Answer Choices:
A. divides
B. divides
C. divides
D. divides
E.
Solution:
The number is greater than and less than . Hence,
is an integer precisely when it is equal to . This implies that , so the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions