MathDB

3

Part of 2013 EGMO

Problems(1)

Constructing sets of positive integers

Source: European Girl's MO 2013, Problem 3

4/10/2013
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.
least common multiplenumber theoryCombinatorial Number TheoryEGMOEGMO 2013