Problem:
For how many integers is the square of an integer?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If , for some , then . Since and have no common factors and is an integer, must be a factor of . This occurs only when , or . The corresponding values of are , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions