Ehrhart polynomials of cyclic polytopes

The Ehrhart polynomial of an integral convex polytope counts the number of lattice points in dilates of the polytope. In (Coefficients and roots of Ehrhart polynomials, preprint), the authors conjectured that for any cyclic polytope with integral parameters, the Ehrhart polynomial of it is equal to its volume plus the Ehrhart polynomial of its lower envelope and proved the case when the dimension d = 2 . In our article, we prove the conjecture for any dimension.