p^k元域上的方程∑_0^(n-1)a^ix^(n-1-i)=0

∑_0^(n-1)a^ix^(n-1-i)=0 over the Field with p^k Elements

F是pk 元域 ,n是正整数 ,xn -1 +axn -2 +… +an -2 x +an -1 =0 (a≠ 0 )是F上的方程。该文给出该方程在F中的根 :(n ,pk- 1 ) - 1个单根 ,或 (n ,pk- 1 )组互不相同的重根 ,或没有根 ;

The F ?is a field with p k element. The n is a positive interger.The ∑ n-1 0a ix n-1-i =0 (a≠0)is an equation over F.In this paper, the author gives the roots of this equation in F,that is, it has ( n,p k-1)-1 single roots or (n,p k-1) distinct groups of repeated roots,or it has no roots.Then the methods and examples to find roots are given.