Elemental Patterns from the Erdos Straus Conjecture

This paper makes the following conjecture: For every prime p there exists a positive integer x with p4 x p2 and a positive divisor d|x² so that either: (1) d (4x - p) -px; or (2) d x and d (4x - p) -x. Furthermore this paper proves that the solutions to these modular equations are in one-to-one correspondence with the solutions of the diophantine equation used in the Erdos Straus conjecture.