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We study the unique solvability of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x| ^a . Depending on the value of the parameter a, we prove a uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet–Navier problem in the exterior of a compact set.