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coloring all postitive integers red or green

Source: Czech-Polish-Slovak Junior Match 2013, Individual p2 CPSJ

March 14, 2020
ColoringcombinatoricsSum

Problem Statement

Each positive integer should be colored red or green in such a way that the following two conditions are met: - Let nn be any red number. The sum of any nn (not necessarily different) red numbers is red. - Let mm be any green number. The sum of any mm (not necessarily different) green numbers is green. Determine all such colorings.
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