Can Flat Spectrum Radio Quasars make most of the overall gamma--ray background?

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The contribution of discrete sources to the gamma--ray background is modeled. Flat spectrum radio quasars are known to make a substantial contribution to the hard (E > 100 MeV) background. The so called ``MeV bump", however, cannot be accounted for in terms of known classes of sources even taking into account the newly discovered class of objects with a broad band spectrum sharply peaked in the MeV range (``MeV blazars"). Even in the most optimistic case the predicted intensity falls short of at least a factor three.