多項(xiàng)式的帶余除法及同余問題

多項(xiàng)式的帶余除法及同余問題

摘  要：主要介紹了多項(xiàng)式帶余除法、整除的概念、性質(zhì)及求解多項(xiàng)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(xiàng)式的性質(zhì)、代定系數(shù)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(xiàng)式同余的概念、性質(zhì)；多項(xiàng)式的剩余類，包括剩余類加群、剩余類環(huán)．
關(guān)鍵詞：多項(xiàng)式；整除；同余；剩余類；剩余類環(huán)．

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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