Question 86
Each of the numbers in the set $A=\{1,2, \ldots, 2017\}$ 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.
(Inspired by Problem 891 from Putnam and Beyond, T. Andreescu and R. Gelca, Springer (2007))
(Inspired by Problem 891 from Putnam and Beyond, T. Andreescu and R. Gelca, Springer (2007))