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Olimpiada de Mayo(OMA) 2017

Source: May Olympiad(Olimpiada de Mayo) 2017

October 2, 2017
algebra

Problem Statement

Alice writes differents real numbers in the board, if a,b,ca,b,c are three numbers in this board, least one of this numbers a+b,b+c,a+ca + b, b + c, a + c also is a number in the board. What's the largest quantity of numbers written in the board???
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