  An N-body bosonic model with delta-contact interactions projected on the
lowest Landau level is considered. For a given number of particles in a given
angular momentum sector, any energy level can be obtained exactly by means of
diagonalizing a finite matrix: they are roots of algebraic equations. A
complete solution of the three-body problem is presented, some general
properties of the N-body spectrum are pointed out, and a number of novel exact
analytic eigenstates are obtained. The FQHE N-fermion model with
Laplacian-delta interactions is also considered along the same lines of
analysis. New exact eigenstates are proposed, along with the Slater
determinant, whose eigenvalues are shown to be related to Catalan numbers.
