x^n- x- a的不可约二次因式(英文)

The irreducible quadratic factors of x^n-x-a

设 f ( x) =xn-x-a∈ Z[x],其中 a≠ 0 .本文证明了 :当 n>6时 ,如果 f ( x)在 Z[x]中有首项系数1的不可约二次因式 n≡ 2 ( mod6) ,a=-1 ,g( x) =x2 -x+1或 n=7,a=± 2 80 ,g( x) =x2

Let f(x)=x n-x-a∈Z,where a≠0. We p rove that if n>6 and f(x) has an irreducible quadratic factor g(x) i n Z which is monic,then either n≡2(mod 6),a=-1 and g(x)=x 2-x+1,or,n=7,a=±280 and g(x)=x 2x+5.