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4

Part of 2005 Balkan MO

Problems(1)

balkan 2005-4

Source:

5/6/2005
Let n≥2n \geq 2 be an integer. Let SS be a subset of {1,2,…,n}\{1,2,\dots,n\} such that SS neither contains two elements one of which divides the other, nor contains two elements which are coprime. What is the maximal possible number of elements of such a set SS?
combinatorics unsolvedcombinatorics