  Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in
the j -orbit) are functions of two-body energies. In some cases they are linear
combinations of two-body energies whose coe+/-cients are independent of the
interaction and are rational non-negative num- bers. It is shown here that a
state which is an eigenstate of any two-body interaction has this solvability
property. This includes, in particular, any state with spin J if there are no
other states with this J in the jn configuration. It is also shown that
eigenstates with solvable eigenvalues have definite seniority v and thus,
exhibit partial dynamical symmetry.
