  The vertex set of the kth cartesian power of a directed cycle of length m can
be naturally identified with the set of k-tuples of integers modulo m. For any
two vertices v and w of this graph, it is easy to see that if there is a
hamiltonian path from v to w, then the sum of the coordinates of v is
congruent, modulo m, to one more than the sum of the coordinates of w. We prove
the converse, unless k = 2 and m is odd.
