In conventional superconductors, the interaction that pairs the electrons to form the superconducting state is mediated by lattice vibrations¹ (phonons). In high-transition-temperature (high-T_c) copper oxides, it is generally believed that magnetic excitations might play a fundamental role in the superconducting mechanism because superconductivity occurs when mobile 'electrons' or 'holes' are doped into the antiferromagnetic parent compounds². Indeed, a sharp magnetic excitation termed 'resonance' has been observed by neutron scattering in a number of hole-doped materials^{3, 4, 5, 6, 7, 8, 9, 10, 11}. The resonance is intimately related to superconductivity¹², and its interaction with charged quasi-particles observed by photoemission^{13, 14}, optical conductivity¹⁵, and tunnelling¹⁶ suggests that it might play a part similar to that of phonons in conventional superconductors. The relevance of the resonance to high-T_c superconductivity, however, has been in doubt because so far it has been found only in hole-doped materials¹⁷. Here we report the discovery of the resonance in electron-doped superconducting Pr_0.88LaCe_0.12CuO_4- (T_c = 24 K). We find that the resonance energy (E_r) is proportional to T_c via E_r 5.8k_BT_c for all high-T_c superconductors irrespective of electron- or hole-doping. Our results demonstrate that the resonance is a fundamental property of the superconducting copper oxides and therefore must be essential in the mechanism of superconductivity.