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-Orozco1,2 and Javier Gomez-Calderon1,2

 1Department of Mathematics, Southwest Texas State University, San Marcos 78666-4603, Texas , USA
2Department of Mathematics, The Pennsylvania State University, New Kensington Campus, New Kensington 15068, Pennsylvania, USA
Received 28 May 1992; Revised 19 April 1993

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.