Each of the numbers in the set \(A = \{1,2, \cdots, 2017\}\) is colored either red or white. Prove that for \(n \geq 18\), there exists a coloring of the numbers in \(A\) such that any of its n-term arithmetic sequences contains both colors.
Source: Philippine Mathematical Olympiad
Tags: combinatorics, arithmetic sequence, Coloring
Each of the numbers in the set \(A = \{1,2, \cdots, 2017\}\) is colored either red or white. Prove that for \(n \geq 18\), there exists a coloring of the numbers in \(A\) such that any of its n-term arithmetic sequences contains both colors.