ON PRIMITIVE ELEMENTS IN FINITE FIELDS AND ON ELLIPTIC CURVES

Abstract

An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)Fp[x], is obtained, "on the average" over all polynomials f of fixed degree, and an estimate for the number of "sparse" factorable polynomials is also obtained.