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Pairwise products form arithmetic progression

Source: Kyiv City MO 2022 Round 1, Problem 11.4

January 23, 2022
algebraArithmetic Progressionarithmetic sequence

Problem Statement

You are given n≥4n\ge 4 positive real numbers. It turned out that all n(n−1)2\frac{n(n-1)}{2} of their pairwise products form an arithmetic progression in some order. Show that all given numbers are equal.
(Proposed by Anton Trygub)
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