Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body system

An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their algebraic resolvability is proven. The supersymmetric generalization is used to build a novel integrable isospin extension of the Ruijsenaars-Schneider three-body system.