Problem:
Let , and be nonnegative integers such that . What is the maximum value of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that
where , and are positive integers whose sum is . A case-by-case analysis shows that pqt is largest when two of the numbers are and the third is . Thus the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions