Research and application of Chinese remainder theorem

Abstract

The Chinese remainder theorem (denoted it as " the theorem" in this article) was originally an important theorem in number theory. It played a vital role in the integer solution of the congruence equation in ancient times. With the continuous development of the algebraic system, the theorem naturally has different forms. This paper will show some research and applications based on the theorem. For example, the theorem in polynomial form, the theorem in the form of group theory, the theorem on unitary rings, the theorem on polynomial ring modules, etc. It is not difficult to know that integers and polynomials are special rings, so this the two forms of the theorem are the theorems that can be covered on the unitary ring. In fact, the theorem in the form of group theory is also covered. This paper will elaborate the first three forms of the theorem and give their specific applications.