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Gamma-ray bursts (GRBs) and following afterglows are considered to beproduced by dissipation of kinetic energy of a relativistic fireball andradiation process is widely believed as synchrotron radiation or inverseCompton scattering of electrons. We argue that the transfer of kinetic energyof ejecta into electrons may be inefficient process and hence the total energyreleased by a GRB event is much larger than that emitted in soft gamma-rays, bya factor of \sim (m_p/m_e). We show that, in this case, very strong emission ofTeV gamma-rays is possible due to synchrotron radiation of protons acceleratedup to \sim 10^{21} eV, which are trapped in the magnetic field of afterglowshock and radiate their energy on an observational time scale of \sim day. Thissuggests a possibility that GRBs are most energetic in TeV range and such TeVgamma-rays may be detectable from GRBs even at cosmological distances, i.e., z\sim 1, by currently working ground-based telescopes. Furthermore, this modelgives a quantitative explanation for the famous long-duration GeV photonsdetected from GRB940217. If TeV gamma-ray emission which is much more energeticthan GRB photons is detected, it provides a strong evidence for acceleration ofprotons up to \sim 10^{21} eV.Comment: 10 pages, no figure. To appear in ApJ Letter

Very Strong T[CLC]e[/CLC]V Emission as Gamma-Ray Burst Afterglows