P^K元域F及其单超越扩域E上的四类方程

The Four Classes of Equations over a Field with P^K Elements F and a Simple Transcendental Extension Field E of F

本文讨论 PK元域 F及其单超越扩域 E上的二次方程、三次方程、二项方程、三项方程 ,给出方程在 F及 E上有根或没有根的条件 ,若方程有限 ,则给出根的个数与求根的方法 。

In this paper,the author discusses quadric, cubic,binomial,trinomial equation over a field with p K elements F and a simple transcendental extension field E of F. This gives the conditions that every equation has roots or has no roots in F and E.If the equation has roots, then the number of its roots and the method to find roots are given.These rusults are applied in the combination design.