Matrix powers over finite fields
Maria T. Acosta-De-Orozco, Javier Gomez-Calderon · International Journal of Mathematics and Mathematical Sciences · 1992
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.