ABSTRACT
Solving linear congruences is fundamental in many parts of number theory. The generalization, solving polynomial congruences, is perhaps not as basic but is still an important topic. For the polynomials students have worked with in the past, namely polynomials with rational, real, or complex coefficients, the number of solutions in complex numbers is at most the degree of the polynomial. How to solve polynomial congruences mod primes and mod prime powers, the Chinese Remainder Theorem allows solving polynomial congruences for composite moduli. Newton—Raphson Method process can be continued with the hope of getting even better approximations to solutions. The same idea works when solving polynomial congruences mod prime powers. When students are work with polynomials whose coefficients are rational or real numbers. A quadratic polynomial has at most two rational or real roots, but may have none.
