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Xvii cono sur [argentina 2006] q3.

Source: Spanish Communities

May 11, 2006
inequalitiesnumber theory proposednumber theory

Problem Statement

Let nn be a natural number. The finite sequence α\alpha of positive integer terms, there are nn different numbers (α\alpha can have repeated terms). Moreover, if from one from its terms any we subtract 1, we obtain a sequence which has, between its terms, at least nn different positive numbers. What's the minimum value of the sum of all the terms of α\alpha?
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