MathDB
Macedonian JBMO TST 2014, Problem 5

Source:

March 30, 2015
Setscombinatorics

Problem Statement

Prove that there exist infinitely many pairwisely disjoint sets A(1),A(2),...,A(2014)A(1), A(2),...,A(2014) which are not empty, whose union is the set of positive integers and which satisfy the following condition: For arbitrary positive integers aa and bb, at least two of the numbers aa, bb and GCD(a,b)GCD(a,b) belong to one of the sets A(1),A(2),...,A(2014)A(1), A(2),...,A(2014).
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