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 can the set of natural numbers be colored in 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?