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As a consequence of the electrostatic nature of the electron longitudinal optical phonon interaction, the electron-phonon interaction matrix is independent of the mass of the electron. On the other hand the dimensionless coupling constant α does depend on this mass. This fact enables us to establish a generalization of the 1: 2: 3: 4 theorem of Pekar for the whole range of the coupling constant and to derive a ground state theorem for free polarons which relates the long wavelenght behaviour of the current-current correlation function with the ground state energy.