Primitive Elements of Galois Extensions of Finite Fields

Abstract

Abstract. As is well known, N?(«) = (1/n) J2d\n ß{d)q"ld coincides with the number of monic irreducible polynomials of GF(q)[X] of degree n . In this note we discuss the curve nNx(n) and the solutions of equations nNx(n) = b (b > n) . As a corollary of these results, we present a necessary and sufficient arithmetical condition for R/K to have a primitive element.