Quadratic Polynomials with Coefficients

Abstract

This research explores the properties and solutions of quadratic polynomials where the coefficients are considered modulo n, for various integers n. The study investigates the number of roots, their properties, and the conditions for solvability in modular arithmetic. Theoretical analysis is combined with computational examples to illustrate the findings. The results contribute to a deeper understanding of polynomial equations in modular rings, which have applications in number theory, cryptography, and computer science.