Problem:
How many positive perfect squares less than are divisible by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because 5 is prime, a perfect square is divisible by 5 if and only if its square root is divisible by 5 . Note that , so , and are the only positive perfect squares satisfying the given condition. There are such numbers.
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions