Problem:
Suppose that
is an integer. Which of the following statements must be true about ?
Answer Choices:
A. It is negative.
B. It is even, but not necessarily a multiple of .
C. It is a multiple of , but not necessarily even.
D. It is a multiple of , but not necessarily a multiple of .
E. It is a multiple of .
Solution:
Because
is an integer, must be even. The case shows that is not necessarily a multiple of and that none of the other statements must be true.
The problems on this page are the property of the MAA's American Mathematics Competitions