We present magneto-optical studies on a high-density two-dimensional electron gas system. Low-temperature magnetoluminescence spectra of a GaAs/InxGa1-xAs/AlyGa1-yAs modulation-doped single-quantum-well structure reveal several features related to Landau-level transitions and corresponding LO-phonon satellite emissions. The coupling between these two families of transitions results in clearly identifiable resonant magnetopolaron effects. The observed anticrossing splitting energy value agrees quantitatively with theoretical models that take into account the presence of the electron gas. Additionally, the peak intensity of transitions at the Fermi energy exhibits a pronounced oscillatory behavior with magnetic fields. These oscillations are attributed to even filling factors.54161136011364