Problem:
Let be three integers such that is an arithmetic progression and is a geometric progression. What is the smallest possible value for ?
Answer Choices:
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Solution:
Let be the common difference of the arithmetic progression. Then , and because is a geometric progression,
Thus , which simplifies to . Because , it follows that and therefore and for some positive integer . Thus , and the smallest value of is .
The problems on this page are the property of the MAA's American Mathematics Competitions