On the Existence of Rainbow 4-Term Arithmetic Progressions

Abstract

For infinitely many natural numbers n, we construct 4-colorings of [n] = {1, 2, . . ., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungić et al. (Comb Probab Comput 12:599–620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).

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