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以前各作者發表过不少关于多項式不可約的充分条件(判別法)。但是在数学文献里却沒有比较簡單的有关多項式可約或不可約的充要条件。 現在这篇論文里証明了某些带有代数及数論性質的命題,它們建立了数的相等和多項式恆等之間的相互联系。从命題的証明中,作为推論就得到很簡單的多項式的可約或不可約的充要条件;在可約的情况下,可能找出任一多項式的因式分解,这些因式在有理数体上是可約的。定理1.設
Previous authors have published many sufficient conditions (discriminative methods) for polynomial irreducibility. However, in the mathematics literature, there is no simple and sufficient condition about the polynomial contraction or irreducibility. This paper now proves certain propositions with algebraic and numerical properties that establish the interconnection between equality of numbers and polynomial identity. From the proof of the proposition, as a corollary, a sufficient and necessary condition for a simple polynomial to be reducible or irreducible is obtained; in the case of reducibility, it is possible to find the factorization of any polynomial that is on a rational number basis. It is contractible. Theorem 1. Set