  The constant pairing Hamiltonian holds exact solutions worked out by
Richardson in the early Sixties. This exact solution of the pairing Hamiltonian
regained interest at the end of the Nineties. The discret complex-energy states
had been included in the Richardson's solutions by Hasegawa et al. [1]. In this
contribution we reformulate the problem of determining the exact eigenenergies
of the pairing Hamiltonian when the continuum is included through the single
particle level density. The solutions with discret complex-energy states is
recovered by analytic continuation of the equations to the complex energy
plane. This formulation may be applied to loosely bound system where the
correlations with the continuum-spectrum of energy is really important. Some
details are given to show how the many-body eigenenergy emerges as sum of the
pair-energies.
