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n + 1 different numbers among 1-2n, exist >=2, one divides another

Source: Spanish Mathematical Olympiad 1971 P8

December 5, 2022
number theorydivides

Problem Statement

Among the 2n2n numbers 1,2,3,...,2n1, 2, 3, . . . , 2n are chosen in any way n+1n + 1 different numbers. Prove that among the chosen numbers there are at least two, such that one divides the other.
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