Problem:
The product of three positive integers is times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of .
Solution:
Call the three integers , and , and, without loss of generality, assume . Then , and . Thus , and , so , or , and , or . The sum of the possible values of is .
The problems on this page are the property of the MAA's American Mathematics Competitions