  The gamma-rays from gamma-ray bursts (GRBs) are believed to be produced by
internal shocks driven by small timescale, ~1 ms, variation in the GRB
outflows, and a pair-production spectral cutoff is generally expected around
the GeV range. However, the observed optical flashes accompanying GRBs suggest
that the delayed residual collisions due to large timescale variation continue
to accelerate electrons. We show here that the inverse-Compton (IC) scattering
of the prompt gamma-rays by these residual internal shock electrons leads to a
high energy emission beyond the previously thought spectral cutoff, in
agreement with the previous detections of GeV photons by EGRET in several GRBs
in conjunction with MeV emission. We expect a spectral break due to the
transition from the primary to residual internal shock emission at the
previously thought spectral cutoff, and expect systematic time delays of high
energy photons relative to MeV emission, the discovery of which would provide
stringent constraint on the outflow properties, but requires large enough
collection of high energy photons by, e.g., Fermi and AGILE satellites.
  The recent Fermi-detected bright GRB 080916c unambiguously shows the shifting
of the prompt emission toward later times as the photon energy increases, as
predicted in the residual collision model. The detected prompt, highest energy
photon (about 70 GeV in the rest frame of the GRB) may not be produced by
primary internal shocks but by IC emission in residual collisions. With the
method involving time delays of high energy emission, the bulk Lorentz factor
of GRB 080916c is determined to be \Gamma ~ 300.
