On Rainbow Arithmetic Progressions

  • Maria Axenovich
  • Dmitri Fon-Der-Flaass

Abstract

Consider natural numbers $\{1, \cdots, n\}$ colored in three colors. We prove that if each color appears on at least $(n+4)/6$ numbers then there is a three-term arithmetic progression whose elements are colored in distinct colors. This variation on the theme of Van der Waerden's theorem proves the conjecture of Jungić et al.

Published
2004-01-02
Article Number
R1