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We exactly analyze, on the mean-field level, the low-momentum properties of asingle impurity atom loaded in the dilute one-dimensional Bose gas with two-and three-body short-range interactions. Particularly the Bose polaron bindingenergy and the quasiparticle residue are calculated for the considered systemin the broad region of parameters change. We also explore the genericmean-field formula for the polaron effective mass which was shown to depend onthe density profile of bath particles with a motionless impurity immersed.

Mean-field properties of impurity in Bose gas with three-body forces