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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 3, Pages 539-544

On the matrix equation Xn=B over finite fields

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

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 BM.