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Well, the least possible positive integers are 1, 2, 3 - but that would not give you a valid triangle, so you need to increase at least one of those numbers. Increasing only one of these numbers, or even two of them, doesn't work, so the smallest set of such integers would be 2, 3, 4.

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Q: A triangle with integer length sides has no two sides equal. What is its least possible perimeter?
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