论文标题
二次形式的一对原始元素，在有限场上有规定的痕迹
Pair of primitive elements in quadratic form with prescribed trace over a finite field
论文作者
论文摘要
在本文中，我们为存在原始元素$α\ in \ fm $建立了足够的条件\ fm（x）$，使得$ b^2-4ac \ neq 0 $。我们得出的结论是，对于$ m \ geq 5 $，只有一个异常对$（q，m）$，即$（2,6）$。
In this article, we establish a sufficient condition for the existence of primitive element $α\in \Fm$ is such that $f(α)$ is also primitive element of $\Fm$ and $Tr_{\Fm/\F}(α)=β$, for any prescribed $β\in\F$, where $f(x)= ax^2 + bx + c\in \Fm(x)$ such that $b^2-4ac\neq 0$. We conclude that, for $m\geq 5$ there is only one exceptional pair $(q,m)$ which is $(2,6)$.
