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Pairs with close sums

Source: Kyiv City MO 2023 Round 1, Problem 11.2

December 16, 2023
algebra

Problem Statement

You are given n≥4n\geq 4 positive real numbers. Consider all n(n−1)2\frac{n(n-1)}{2} pairwise sums of these numbers. Show that some two of these sums differ in at most 2n−2\sqrt[n-2]{2} times.
Proposed by Anton Trygub
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