摘要
设 GF(g)为一有限域,a 和 b 为域中单位,柯亨曾证明:除去有限个q的例外值,GF(q)中存在本原元ξ使得 aξ+b 可表示一个非零的三次幂剩余。本文将这一结果推广到任意的 d 次幂剩余,证明了更为一般的结果。
Let GF(q) denote the finite field of prime power order q,where a and b are units.Cohen proved that except for finite q as exceptional values,there are some primi- tive elements (roots) ξ of GF(q) such that aξ+b can be used to represent a nonzero cubic power residue.In this paper it is shown that his result is a special case of a much more gen- eral one which states that each of d-th power residues has at least one of representations of the form aξ+b where ξ is a primitive element.
