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Are Numbers on the Circle Always Equal

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 9.1

April 5, 2023
combinatoricsequality

Problem Statement

n≥4n \ge 4 real numbers are arranged in a circle. It turned out that for any four consecutive numbers a,b,c,da, b, c, d, that lie on the circle in this order, holds a+d=b+ca+d = b+c. For which nn does it follow that all numbers on the circle are equal?
Proposed by Oleksiy Masalitin
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