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problem from Austrian - Polish Math Competition

Source:

December 17, 2010
combinatorics unsolvedcombinatorics

Problem Statement

Does the set {1,2,3,...,3000}\{1,2,3,...,3000\} contain a subset A A consisting of 2000 numbers that x∈Ax\in A implies 2x∉A2x \notin A ?!! :?:
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