2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/177252A dispersion relation for electromagnetic wave propagation in a strongly magnetized cold plasma is deduced, taking photon-photon scattering into account. It is shown that the combined plasma and quantum electrodynamic effect is important for understanding the mode-structures in magnetar and pulsar atmospheres. The implications of our results are discussed.6 pages, 1 figure, to appear in New Journal of PhysicsAstrophysicstext