Let A and B be two disjoint subsets of positive integers such that |Al=n, lBl= m. It is known that for any k Є AUB at least one of the two following conditions holds 1) k + 17 Є A 2) k -31 Є B Find all possible values of m/n.
Source: Belarusian Mathematical Olympiad 67th
Tags: algebra
Let A and B be two disjoint subsets of positive integers such that |Al=n, lBl= m. It is known that for any k Є AUB at least one of the two following conditions holds 1) k + 17 Є A 2) k -31 Є B Find all possible values of m/n.