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Summary form only given. We report on experiments ongoing on a quantum degenerate mixture composed of a Fermi gas of potassium atoms and a Bose-Einstein condensate of rubidium atoms. The large interspecies attraction makes this system appealing for the study of strongly interacting Fermi-Bose gases. A first effect of the direct boson-fermion attraction is a modification of the ground state of the mixture trapped in a magnetic potential, which can eventually lead to a dynamical instability towards a simultaneous collapse of the mixture above critical atom numbers, as we recently observed. A secondary effect of the interaction is the appearance of an effective attraction between fermions, which is predicted to result in a boson-induced Cooper pairing of fermions. We are presently studying the way of producing a stable mixture of two different spin states of fermions with the bosons to investigate this phenomenon.