p^k元域及其单超越扩域上的二项方程三项方程和因式方程

The Binomial Equations and Three-term Equations and Factor Equations Over the Field of pk Elements and Its Simple Transcendental Extension Field

设F是pk元域,E是F的单超越扩域.综述了F与E上的二项方程、三项方程和因式方程,给出了方程在F与E中有根或没有根的条件,若方程有根,则给出根的个数与根的求法.

Let F is the field of p^k elements and E is simple transcendental extension field of the F. In this paper,the author desctibes binomial equations, three-term equations and factor equations over the F and E,and gives the conditions that every equation has roots or has no roots in the F and E. If the equation has roots,then the number of its roots and method to find roots are given. These rusults are applied in combination design.