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2000 -element subset of 1-3000 where none of them is twice another

Source: Portugal OPM 1998 p3

May 18, 2024
combinatorics

Problem Statement

Could the set {1,2,3,...,3000}\{1,2,3,...,3000\} contain a subset of 20002000 elements such that none of them is twice the size of another?
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