Problem:
For how many positive integers  does there exist at least one positive integer  such that 
Answer Choices:
A.  
B.  
C.  
D.  
E. infinitely many 
Solution:
When , the inequality becomes , which is satisfied by all integers . Thus, there are infinitely many of the desired values of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions