有理数域上的两类不可约多项式

Two Classes of Irreducible Polynomials in Rational Field

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.

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）= ∏i=1^n （x-ai）^2m ＋1 is irreducible in Q. Inspired by Schur conjecture, two classes of irreducible polynomials in Q were constructed by elementary method.