Problem:
What is the largest integer that is a divisor of
for all positive even integers
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Among five consecutive odd numbers, at least one is divisible by and exactly one is divisible by , so the product is always divisible by . The cases , and demonstrate that no larger common divisor is possible, since is the greatest common divisor of , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions