  Masuoka proved that for a prime p, semisimple Hopf algebras of dimension 2p
over an algebraically closed field k of characteristic 0, are trivial (i.e. are
either group algebras or the dual of group algebras). Westreich and the second
author obtained the same result for dimension 3p, and then pushed the analysis
further and among the rest obtained the same result for semisimple Hopf
algebras H of dimension pq so that H and H^* are of Frobenius type (i.e. the
dimensions of their irreducible representations divide the dimension of H).
They concluded with the conjecture that any semisimple Hopf algebra H of
dimension pq over k, is trivial. In this paper we use Theorem 1.4 in our
previous paper q-alg/9712033 to prove that both H and H^* are of Frobenius
type, and hence prove this conjecture.
