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Constructing sets of positive integers

Source: European Girl's MO 2013, Problem 3

April 10, 2013
least common multiplenumber theoryCombinatorial Number TheoryEGMOEGMO 2013

Problem Statement

Let nn be a positive integer.
(a) Prove that there exists a set SS of 6n6n pairwise different positive integers, such that the least common multiple of any two elements of SS is no larger than 32n232n^2.
(b) Prove that every set TT of 6n6n pairwise different positive integers contains two elements the least common multiple of which is larger than 9n29n^2.
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