### A counterexample to a conjecture of Drużkowski and Rusek

Let F = X + H be a cubic homogeneous polynomial automorphism from ${\u2102}^{n}$ to ${\u2102}^{n}$. Let $p$ be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that $deg{F}^{-1}\le {3}^{p-1}$. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.