  We consider a simple model for an SNS Josephson junction in which the "normal
metal" is a section of a filling-factor $\nu=2$ integer quantum-Hall edge. We
provide analytic expressions for the current/phase relations to all orders in
the coupling between the superconductor and the quantum Hall edge modes, and
for all temperatures. Our conclusions are consistent with the earlier
perturbative study by Ma and Zyuzin [Europhysics Letters {\bf 21} 941-945
(1993)]: The Josephson current is independent of the distance between the
superconducting leads, and the upper bound on the maximum Josephson current is
inversely proportional to the perimeter of the Hall device.
