Circulant Matrices And Polynomials

This thesis is composed of three chapters.It's based on the circulant matrices and the K?nig-Rados theorem,applying to the primality of two polynomials,cyclotomic polynomials and primitive polynomials.In the first chapter,we give some basic and important results about primitive element,unit root,circulant matrix,cyclotomic polynomial,and primitive polynomial.In the second chapter,based on the K?nig-Rados theorem,by discussing the value range,we get the theorem's extension.As applications,the sufficient and necessary conditions for xf)(to be coprime with-1mx is obtained.(Conditions and value range have close relations,so we have to discuss according to value range).We also provide the alternative approaches to factorizing xf)(as well as to determining whether xf)(is a cyclotomic polynomial.Similarly,we get the sufficient and necessary conditions of the primitive polynomial.In the last chapter,we summarize the results we obtained and put forward some problems for future investigation.