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Iberoamerican Olympiad 2013 - Problem 5

Source: http://oim2013.opm.org.pa/pdfs/examen_pt.pdf

August 13, 2014
number theory proposednumber theory

Problem Statement

Let AA and BB be two sets such that A∪BA \cup B is the set of the positive integers, and A∩BA \cap B is the empty set. It is known that if two positive integers have a prime larger than 20132013 as their difference, then one of them is in AA and the other is in BB. Find all the possibilities for the sets AA and BB.
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