The Horicianu Modular Inverse Algorithm: A Forward-Substitution Approach

This paper formalizes the Horicianu Modular Inverse Algorithm (HMIA), a streamlined method for calculating modular inverses. While traditional methods like the Extended Euclidean Algorithm (EEA) rely on tracking multiple sequences of coefficients or performing a "backward" substitution, the Horicianu method employs a "forward" substitution logic. By accumulating a product of quotients and applying a final sign correction based on the chain length, the algorithm offers a reduced variable state and enhanced pedagogical clarity.