Problem:
In the year 2001, the United States will host the International Mathematical Olympiad. Let , and be distinct positive integers such that the product . What is the largest possible value of the sum ?
Answer Choices:
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Solution:
Factor into primes to get . The largest possible sum of three distinct factors whose product is the one which combines the two largest prime factors, namely , and , so the largest possible sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions