  The collinear factorization properties of two-loop scattering amplitudes in
dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar
('t Hooft) limit, higher-loop contributions can be expressed entirely in terms
of one-loop amplitudes. We demonstrate this relation explicitly for the
two-loop four-point amplitude and, based on the collinear limits, conjecture an
analogous relation for n-point amplitudes. The simplicity of the relation is
consistent with intuition based on the AdS/CFT correspondence that the form of
the large N_c L-loop amplitudes should be simple enough to allow a resummation
to all orders.
