Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds

On a smooth, closed Riemannian manifold $(M,g)$ of dimension $n\ge 3$ with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to $g$ with constant Q-curvature of order 4 are the metrics $\lambda g$ with $\lambda >0$ constant.