  In this paper we attack the Erdos-Straus conjecture by means of the structure
of its solutions, extending and improving the results of a previous paper.
Using previous results and supported by the works of Elsholtz and Tao and Monks
and Velingker we define a system of congruences for which there are always
solutions to the Erdos-Straus conjecture and which we conjecture to include all
prime numbers. For this purpose, and always taking into account a result due to
Mordell that limits the congruences admitting polynomial identities to those
that are not quadratic residues, we will adopt a transversal approach and
classify the solutions by their form and not by those congruences that produce
them. Thus we define two new types of solutions, which we call Type A and B,
and relate them to the already known Type II solutions and study their
properties. Finally we conjecture that every prime number has at least one
solution of Type A or B and we associate a congruence and a general polynomial
to each Type of solution.
