Problem:
For any positive integer , the notation denotes the product of the integers through . What is the largest integer for which is a factor of the sum
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Factoring yields . The exponent of in is , one for each multiple of and one more for each multiple of . Thus the exponent of in the product is as .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions