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Subset with 4n elements

Source: Problem 2, Brazilian MO 2015

October 20, 2015
combinatorics proposedcombinatorics

Problem Statement

Consider S={1,2,3,⋯ ,6n}S=\{1, 2, 3, \cdots, 6n\}, n>1n>1. Find the largest kk such that the following statement is true: every subset AA of SS with 4n4n elements has at least kk pairs (a,b)(a,b), a<ba<b and bb is divisible by aa.
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