The Pronic-Quadratic Factorization Method: an approach to factorization, congruences and algebraic relations

This article presents the Pronic-Quadratic Method (PQM), a didactic reparametrization of Fermat’s difference of squares for odd integers, based on relations between perfect squares and pronic numbers. The method organizes factorization into four elementary steps, with parity constraints, a linear adjustment number C, adjacent pronics or squares, and modular filters (bases 10, 9, 11 and 7). It does not change the computational complexity of integer factorization. Worked examples include N = 105, 75, 2041 and 408 508 091.