International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 767-771
doi:10.1155/S0161171292000991
Matrix powers over finite fields
Maria T. Acosta-de-Orozco1
and Javier Gomez-Calderon2
1Department of Mathematics, Penn State University, Beaver Campus, Monaca 15061, Pennsylvania, USA
2Department of Mathematics, Penn State University, New Kensington Campus, New Kensington 15068, Pennsylvania, USA
Abstract
Let GF(q) denote the finite field of order q=pe with p odd. Let M denote the ring of 2×2 matrices with entries in GF(q). Let n denote a divisor of q−1 and assume 2≤n and 4 does not divide n. In this paper, we consider the problem of determining the number of n-th roots in M of a matrix B∈M. Also, as a related problem, we consider the problem of lifting the solutions of X2=B over Galois rings.