  We compute a minimal bigraded resolution of the Rees Algebra associated to a
proper rational parametrization of a monomial plane curve. We describe
explicitly both the bigraded Betti numbers and the maps of the resolution in
terms of a generalized version of the Euclidean Algorithm. We also explore the
relation between pencils of adjoints of the monomial plane curve and elements
in a suitable piece of the defining ideal of the Rees Algebra.
