The ${\rm Jacobian Conjecture}_{2n}$ implies the ${\rm Dixmier   Problem}_n$
  Using the author's inversion formula for automorphisms of the Weyl algebras with polynomial coefficients and the bound on its degree a slightly shorter (algebraic) proof is given of the result of A. Belov-Kanel and M. Kontsevich that the Jacobian Conjecture implies the Dixmier Proplem. No originality is claimed. 
V. V. Bavula