Problem:
Which of the following numbers is a perfect square?
Answer Choices:
A. 214!15!β
B. 215!16!β
C. 216!17!β
D. 217!18!β
E. 218!19!β
Solution:
Note that 2n!(n+1)!β=(n!)2β
2n+1β, which is a perfect square if and only if 2n+1β is a perfect square. Only choice Dβ satisfies this condition.
The problems on this page are the property of the MAA's American Mathematics Competitions