MathDB
k colors for natural numbers

Source: VI Soros Olympiad 1990-00 R3 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
combinatoricsnumber theory

Problem Statement

For what values of k2k\ge2 can the set of natural numbers be colored in kk colors in such a way that it contains no single - color infinite arithmetic progression, but for any two colors there is a progression whose members are each colored in one of these two colors?