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We have found an expression for the full many-body Green's function of Npairwise finite-range interacting atoms, in a form of a chain fractioninvolving two-body T-matrices only, with no explicit presence of theinteraction potentials themselves. We show that in the limit of infinitelysmall potential range, this expression reduces to the Green's function for Natoms interacting via a generalized pseudo-potential, function of a freeparameter \Lambda. Using this \Lambda-freedom we resolve all inconsistensies ofthe Hartree-Fock-Bogoliubov formalism known so far, with no ad hocmodifications of the theory.Comment: RevTex, 4 pages, no figures; identical copy of the published versio

Rigorous Approach to the Problem of Ultraviolet Divergencies in Dilute Bose Gases