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Set Elements as K-Element Sums

2800MasterCombinatoricsAlgebra

International Mathematical Olympiad

Let $k \geqslant 2$ be an integer. Find the smallest integer $n \geqslant k+1$ with the property that there exists a set of $n$ distinct real numbers such that each of its elements can be written as a sum of $k$ other distinct elements of the set.
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