We study magnetoresistivity oscillations in a high-mobility two-dimensional electron system subject to both microwave and dc electric fields. First, we observe that the oscillation amplitude is a periodic function of the inverse magnetic field and is strongly suppressed at microwave frequencies near half-integers of the cyclotron frequency. Second, we obtain complete conditions for the differential resistivity extrema and saddle points. These findings indicate the importance of scattering without microwave absorption and a special role played by microwave-induced scattering events antiparallel to the electric field.
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