Problem:
For how many positive integers less than or equal to is evenly divisible by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since
the condition is equivalent to having an integer value for
This reduces, when , to having an integer value for
This fraction is an integer unless is an odd prime. There are odd primes less than or equal to , so there are numbers less than or equal to that satisfy the condition.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions