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Pairwise not divided

Source: 2019 China TST Test 4 P4

March 29, 2019
number theory

Problem Statement

Prove that there exist a subset AA of {1,2,⋯ ,2n}\{1,2,\cdots,2^n\} with nn elements, such that for any two different non-empty subset of AA, the sum of elements of one subset doesn't divide another's.
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