Let the torus T^2n be equipped with the standard symplectic
structure and a Hamiltonian H that is periodic in the time variable.
A  subharmonic solution is a periodic orbit of the Hamiltonian flow
with minimal period an integral multiple m of the period of H, with
m>1.
    We prove: If the Hamiltonian flow has only finitely many orbits
with the same period as H, then there are subharmonic solutions with
arbitrarily high minimal period.   Thus there are always infinitely
many distinct periodic orbits.  This was proved in the nondegenerate
case by Conley and Zehnder, and in the case n=2 by Le Calvez.