有理数域上的两类不可约多项式

Two Classes of Irreducible Polynomials in Rational Field

摘要

摘要:受Schur猜想的启发,利用初等数论方法构造出Q上的两类不可约多项式,并指出用此方法可构造出大量的不可约多项式.

Abstract:Let Q be the rational field, about the irreducibility of polynomials in Q, Schur has proposed a famous conjecture: If a1,a2,…,an are different integers, and m>1, thenf(x)=∏ ni=1(x-ai) 2m +1is irreducible in Q. Inspired by Schur conjecture, two classes of irreducible polynomials in Q were constructed by elementary method.