关于x^n-bx-a的二次整系数因式

On the intergral coefficient quadratic factorization of x^n-bx - a

设n≥5,a,b≠0,n∈N,a,b∈Z,利用Gel'found-Baker方法证明了,如果多项中x^n-bx-a有二次整系数因式,则除了n≡2(mod6)且b=1,a=-1,与n≡2(mod3)且b=-1,a=-1这些明显情形外,必定有n<max(exp|b|,512870)。

Let n≥5,a,b≠0, n∈N, a,b∈Z. Using Gel'found-Baker methods, this paper proves that if xn-bx-a has intergral coefficient quadratic factorizations, then n< max (exp |b|, 512870), except cases n=2 (mod3), b = -1,a = -1, and n=2(mod6), b=1,a = -1.