You are given $n\ge 4$ positive real numbers. It turned out that all $\frac{n(n-1)}{2}$ of their pairwise products form an arithmetic progression in some order. Show that all given numbers are equal. (Proposed by Anton Trygub)
Problem
Source: Kyiv City MO 2022 Round 1, Problem 11.4
Tags: algebra, Arithmetic Progression, arithmetic sequence