p^k元域上的方程x^(p^s)-x-c=0

The equation x^(p^s)-x-c=0 over a field with p^k elements

设F是pk元域,s是正整数.给出了方程xps-x-c=0(c∈F)在F中有根的条件及个数.同时研究了有根的xps-x-c=0(c∈F)中元素c的个数及某些多项式xps-x-c(c∈F)的不可约性.

Let F be a field with p^k elements and n be a positive integer. In this paper,the author gives the condition that the equation x^p^s-x-c=0（c∈F）has root in the F and the number of its roots. At the same time, he studies the number of the elements c in the x^p^s-x-c=0（c∈F） having root in the F,and he studies the irreducibility of some polynomial x^p^s-x-c=0（c∈F）,too