  The relation of the recently proposed E(5) critical point symmetry with the
interacting boson model is investigated. The large-N limit of the interacting
boson model at the critical point in the transition from U(5) to O(6) is
obtained by solving the Richardson equations. It is shown explicitly that this
algebraic calculation leads to the same results as the solution of the Bohr
differential equation with a $\beta^4$ potential.
