  We analytically identify a new class of quantum scars protected by
spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They
distinguish from previous (quasi-)static scars by a rigid spectral pairing only
possible in Floquet systems, where strong interaction and drivings equalize the
quasienergy corrections to all scars and maintain their spectral spacings
against generic bilinear perturbations. Scars then enforce the spatial
localization and rigid discrete time crystal (DTC) oscillations as verified
numerically in a trimerized kagome lattice model relevant to recent cold atom
experiments. Our analytical solutions offer a potential scheme to understand
the mechanisms for more generic translation-invariant DTCs.
