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Regional Olympiad - FBH 2017 Grade 11 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

September 19, 2018
Arithmetic ProgressionSetsnumber theory

Problem Statement

Let SS be a set of 66 positive real numbers such that (a,b∈S)(a>b)⇒a+b∈S\left(a,b \in S \right) \left(a>b \right) \Rightarrow a+b \in S or a−b∈Sa-b \in S Prove that if we sort these numbers in ascending order, then they form an arithmetic progression
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