The exact ground-state energy [ital E][sub 0]([Phi]) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length [ital L], threaded by an external flux [Phi]. It includes on-site and nearest-neighbor intersite Coulomb repulsion [ital V], as well as a nonzero bare oxide'' gap [Delta][sub 0] between the orbitals in the unit cell. The correlation exponent [ital K][sub [rho]] of the corresponding low-energy Hamiltonian shows that singlet (extended [ital s]-wave) superconductivity has the most rapidly diverging susceptibility as [ital T][r arrow]0 ([ital K][sub [rho]][gt]1). This superconducting phase is located close to a phase-separation instability of the model, indicated by [ital K][sub [rho]][r arrow][infinity]. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of [ital V] for which [ital K][sub [rho]][gt]1, and slightly broadens the regime of [ital V] where 1[lt][ital K][sub [rho]][lt][infinity].