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Coloring problem with the color pink

Source: Philippine Mathematical Olympiad

December 31, 2017
combinatoricsarithmetic sequenceColoring

Problem Statement

Each of the numbers in the set A={1,2,⋯ ,2017}A = \{1,2, \cdots, 2017\} is colored either red or white. Prove that for n≥18n \geq 18, there exists a coloring of the numbers in AA such that any of its n-term arithmetic sequences contains both colors.
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