多项式的带余除法及同余问题

多项式的带余除法及同余问题

摘  要：主要介绍了多项式带余除法、整除的概念、性质及求解多项式整除的几种方法，包括单位根及因式定理、乘法公式、整除的判别定理、不可约多项式的性质、代定系数法、因式分解的唯1性定理、奇偶分析法、整除的传递性等；多项式同余的概念、性质；多项式的剩余类，包括剩余类加群、剩余类环．
关键词：多项式；整除；同余；剩余类；剩余类环．

The Polynomial Belt-odd Division and Congruence

Abstract:  This paper mainly introduces the polynomial  belt-odd division,the concept of aliquot,the nature and polynomial  aliquot several methods which includes the unit root and the factor theorem,the multiplication formula,the aliquot distinction theorem,the irreducible polynomial nature,the generation decision about the method of correlates,the factorization uniqueness theorem, the odd and even analytic method,the aliquot transitivity and so on; Polynomial  congruence concept,nature;The polynomial  rasidue class,adds the group,the residue class link including the residue class.
 
Keywords:  Polynomial;Aliquot;Congruence;Reside class; Residues ring