International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 539-544
doi:10.1155/S0161171293000663
On the matrix equation Xn=B over finite fields
Maria T. Acosta-de-Orozco
and Javier Gomez-Calderon
Department of Mathematics, Southwest Texas State University, San Marcos 78666-4603, Texas , USA
Abstract
Let GF(q) denote the finite field of order q=pe with p odd and prime. Let M denote the ring of m×m matrices with entries in GF(q). In this paper, we consider the problem of determining the number N=N(n,m,B) of the n-th roots in M of a given matrix B∈M.