On the existence of rainbow 4-term arithmetic progressions

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 Jungic et al. (Comb Probab Comput 12:599-620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).