  We theoretically study dynamic scalar polarizabilities of the ground and
select long-lived excited states of dysprosium, a highly magnetic atom recently
laser cooled and trapped. We demonstrate that there are a set of magic
wavelengths of the unpoarized lattice laser field for each pair of states which
includes the ground state and one of these excited states. At these
wavelengths, the energy shift due to laser field is the same for both states,
which can be useful for resolved sideband cooling on narrow transitions and
precision spectroscopy. We present an analytical formula which, near
resonances, allows for the determination of approximate values of the magic
wavelengths without calculating the dynamic polarizabilities of the excited
states.
