  By applying methods already discussed in a previous series of papers by the
same authors, we construct here classes of integrable quantum systems which
correspond to n fully resonant oscillators with nonlinear couplings. The same
methods are also applied to a series of nontrivial integral sets of functions,
which can be constructed when additional symmetries are present due to the
equality of some of the frequencies. Besides, for n=3 and resonance 1:1:2, an
exceptional integrable system is obtained, in which integrability is not
explicitly connected with this type of symmetry. In this exceptional case,
quantum integrability can be realized by means of a modification of the
symmetrization procedure.
