论文标题
在有限字段上存在一些特殊的原始元素
On existence of some special pair of primitive elements over finite fields
论文作者
论文摘要
在本文中，我们概括了Sharma，Awasthi和Gupta的结果（请参阅\ cite {sag}）。我们在具有$ q = p^k $元素的任何特征的领域工作，我们为存在的原始元素$α\ in \ mathbb {f} _ {p^k} $提供了足够的条件\ mathbb {f} _ {p^k}（x）$是具有一些限制的多项式的商。我们明确地确定了$ k $的值，该$ k $以$ p = 2,3,5 $和$ 7 $存在。
In this paper we generalize the results of Sharma, Awasthi and Gupta (see \cite{SAG}). We work over a field of any characteristic with $q = p^k$ elements and we give a sufficient condition for the existence of a primitive element $α\in \mathbb{F}_{p^k}$ such that $f(α)$ is also primitive in $\mathbb{F}_{p^k}$, where $f(x) \in \mathbb{F}_{p^k}(x)$ is a quotient of polynomials with some restrictions. We explicitly determine the values of $k$ for which such a pair exists for $p=2,3,5$ and $7$.
