有理数域上一类不可约多项式的简单推广

Simple Generalization of a Class of Irreducible Polynomials in Rational Number Field

若a1,a2,…,an是n-1个不同的整数,证明了当n≥4时,f(x)=(x-a1)(x-a2)…(x-an)-1在有理数域Q上不可约;当n≥3时,f(x)=(x-a1)2(x-a2)2…(x-an)2+1在有理数域Q上不可约.

Suppose a1 ,a2,…,an are different Integers of n-1. This paper proves that if n ≥14, the polynomial f（x）= （x-a1） （x-a2）… （x-an）-1 is irreducible in the rational number range Q, and if n≥3, the polynomial f（x） = （x-a1）^2（x-a2）^2…（x-an）^2＋ 1 is irreducible in the rational number range Q.