  The superposition of the Kepler-Coulomb potential on the 3D Euclidean space
with three centrifugal terms has recently been shown to be maximally
superintegrable [Verrier P E and Evans N W 2008 J. Math. Phys. 49 022902] by
finding an additional (hidden) integral of motion which is quartic in the
momenta. In this paper we present the generalization of this result to the ND
spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry
approach that makes use of the curvature parameter. The resulting Hamiltonian,
formed by the (curved) Kepler-Coulomb potential together with N centrifugal
terms, is shown to be endowed with (2N-1) functionally independent integrals of
the motion: one of them is quartic and the remaining ones are quadratic. The
transition from the proper Kepler-Coulomb potential, with its associated
quadratic Laplace-Runge-Lenz N-vector, to the generalized system is fully
described. The role of spherical, nonlinear (cubic), and coalgebra symmetries
in all these systems is highlighted.
