Solving congruence equations using Bernstein forms

TL;DR

This paper introduces a subdivision method based on Bernstein forms to solve systems of congruence equations, extending techniques from polynomial inequalities to modular arithmetic problems.

Contribution

It adapts Bernstein form subdivision methods to efficiently address systems of congruence equations, a novel approach in this context.

Findings

Method is exponential in the number of variables.

Successfully extends polynomial inequality techniques to congruence equations.

Provides a new computational tool for modular systems.

Abstract

We present a subdivision method to solve systems of congruence equations. This method is inspired in a subdivision method, based on Bernstein forms, to solve systems of polynomial inequalities in several variables and arbitrary degrees. The proposed method is exponential in the number of variables.