  Our numerical simulations show that axisymmetric, torsional, magneto-elastic
oscillations of magnetars with a superfluid core can explain the whole range of
observed quasi-periodic oscillations (QPOs) in the giant flares of soft
gamma-ray repeaters. There exist constant phase, magneto-elastic QPOs at both
low (f<150 Hz) and high frequencies (f>500 Hz), in full agreement with
observations. The range of magnetic field strengths required to match the
observed QPO frequencies agrees with that from spin-down estimates. These
results strongly suggest that neutrons in magnetar cores are superfluid.
