Integer colorings with no rainbow 3-term arithmetic progression

In this paper, we study the rainbow Erdős-Rothschild problem with respect to 3term arithmetic progressions. We obtain the asymptotic number of r-colorings of [n] without rainbow 3-term arithmetic progressions, and we show that the typical colorings with this property are 2-colorings. We also prove that [n] attains the maximum number of rainbow 3-term arithmetic progression-free r-colorings among all subsets of [n]. Moreover, the exact number of rainbow 3-term arithmetic progression-free r-colorings of Z_p is obtained, where p is any prime and Z_p is the cyclic group of order p.