  The four longest period Kuiper belt objects have orbital periods close to
integer ratios with each other. A hypothetical planet with orbital period
$\sim$17,117 years, semimajor axis $\sim$665 AU, would have N/1 and N/2 period
ratios with these four objects. The orbital geometries and dynamics of resonant
orbits constrain the orbital plane, the orbital eccentricity and the mass of
such a planet, as well as its current location in its orbital path.
