A gas turbine engine system includes a boost compressor configured to compress air; a combustor in which the compressed air is mixed with fuel and ignited to generate a stream of combustion gases; and a turbine configured to extract energy from the combustion gases, the turbine being drivingly coupled to the boost compressor and to an output shaft via a differential gearbox configured to apportion an input torque from the turbine between a first output torque applied to the output shaft and a second output torque applied to the boost compressor.