Question 17
(ROM 1) Prove that there exists a four-coloring of the set $M=\{1,2,\ldots,1987\}$ such that any arithmetic progression with $10$ terms in the set $M$ is not monochromatic.
Alternative formulation. Let $M=\{1,2,\ldots,1987\}$. Prove that there is a function $f:M\to\{1,2,3,4\}$ that is not constant on every set of $10$ terms from $M$ that form an arithmetic progression.
Alternative formulation. Let $M=\{1,2,\ldots,1987\}$. Prove that there is a function $f:M\to\{1,2,3,4\}$ that is not constant on every set of $10$ terms from $M$ that form an arithmetic progression.