On the matrix equation Xn=B over finite fields - Maria T. Acosta-De-Orozco; Javier Gomez-Calderon (International Journal of Mathematics and Mathematical Sciences)
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.