IMO 1972 LL GBR16

Consider the set S of all the different odd positive integers

imolonglistmathematicsolympiad

IMO 1972 LL GBR16

Origin: GBR

Problem

Consider the set S of all the different odd positive integers that are not multiples of 5 and that are less than 30m, m being a positive integer. What is the smallest integer k such that in any subset of k integers from S there must be two integers one of which divides the other? Prove your result.