Problem:
Let be a positive integer such that is an integer. Which of the following statements is not true:
Answer Choices:
A. $2 divides $
B. $3 divides $
C. $6 divides $
D. $7 divides $
E.
Solution:
The number is greater than 0 and less than . Hence,
is an integer precisely when it is equal to 1 . This implies that , so the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions