Problem:
Suppose that and are positive integers such that . What is the minimum possible value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
An integer is a cube if and only if, in the prime factorization of the number, each prime factor occurs a multiple of three times. Because , the minimum value for is . In that case , and .
The problems on this page are the property of the MAA's American Mathematics Competitions