Integer colorings with forbidden rainbow sums

For a set of positive integers A⊆[n], an r-coloring A is rainbow sum-free if it contains no Schur triple. In this paper we initiate the study Erdős-Rothschild problem in context sets, which asks for subsets [n] with maximum number r-colorings. We show that r=3, interval optimal, while r≥8, [⌊n/2⌋,n] optimal. also prove stability theorem r≥4. The proofs rely on hypergraph container method, and some ad-hoc analysis.