多項式的帶余除法及同余問題

多項式的帶余除法及同余問題

多項式的帶余除法及同余問題

摘  要：主要介紹了多項式帶余除法、整除的概念、性質及求解多項式整除的幾種方法，包括單位根及因式定理、乘法公式、整除的判別定理、不可約多項式的性質、代定系數法、因式分解的唯1性定理、奇偶分析法、整除的傳遞性等；多項式同余的概念、性質；多項式的剩余類，包括剩余類加群、剩余類環．
關鍵詞：多項式；整除；同余；剩余類；剩余類環．

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

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