  We report the experimental results from a dark study and a photo-excited
study of the high mobility GaAs/AlGaAs system at large filling factors, $\nu$.
At large-$\nu$, the dark study indicates several distinct phase relations
("Type-1", "Type-2", and "Type-3") between the oscillatory diagonal- and Hall-
resistances, as the canonical Integral Quantum Hall Effect (IQHE) is manifested
in the "Type-1" case of approximately orthogonal diagonal- and Hall resistance-
oscillations. Surprisingly, the investigation indicates quantum Hall plateaus
also in the "Type-3" case characterized by approximately "anti-phase" Hall- and
diagonal- resistance oscillations, suggesting a new class of IQHE.
  Transport studies under microwave photo-excitation exhibit radiation-induced
magneto-resistance oscillations in both the diagonal, $R_{xx}$, and
off-diagonal, $R_{xy}$, resistances. Further, when the radiation-induced
magneto-resistance oscillations extend into the quantum Hall regime, there
occurs a radiation-induced non-monotonic variation in the amplitude of
Shubnikov-de Haas (SdH) oscillations in $R_{xx}$ \textit{vs}. B, and a
non-monotonic variation in the width of the quantum Hall plateaus in $R_{xy}$.
The latter effect leads into the vanishing of IQHE at the minima of the
radiation-induced $R_{xx}$ oscillations with increased photo-excitation. We
reason that the mechanism which is responsible for producing the non-monotonic
variation in the amplitude of SdH oscillations in $R_{xx}$ under
photo-excitation is also responsible for eliminating, under photo-excitation,
the novel "Type-3" IQHE in the high mobility specimen.
