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IMC 2013/2/4

Source: Imc 2013 Problem 9

August 9, 2013
number theoryIMCcollege contests

Problem Statement

Does there exist an infinite set M\displaystyle{M} consisting of positive integers such that for any a,bāˆˆM\displaystyle{a,b \in M} with a<b\displaystyle{a < b} the sum a+b\displaystyle{a + b} is square-free? Note. A positive integer is called square-free if no perfect square greater than 1\displaystyle{1} divides it.
Proposed by Fedor Petrov, St. Petersburg State University.
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