2009 AMC 8 Problems/Problem 17
Problem
The positive integers and are the two smallest positive integers for which the product of and is a square and the product of and is a cube. What is the sum of and ?
Solution
The prime factorization of . If a number is a perfect square, all of the exponents in its prime factorization must be even. Thus we need to multiply by a 2 and a 5, for a product of 10, which is the minimum possible value of x. Similarly, y can be found by making all the exponents divisible by 3, so the minimum possible value of is . Thus, our answer is .
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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