On primes p for which d divides ord_p(g)

Abstract

Let N_g(d) be the set of primes p such that the order of g modulo p is divisible by a prescribed integer d. Wiertelak showed that this set has a natural density and gave a rather involved explicit expression for it. Let N_g(d)(x) be the number of primes p<=x that are in N_g(d). A simple identity for N_g(d)(x) is established. It is used to derive a more compact expression for the natural density than known hitherto. A numerical demonstration, using a program of Y. Gallot, is presented.

10 pages, 3 tables

References in corpus (1)

• On the distribution of the order and index of g(mod p) over residue classes II

Cited by in corpus (3)

• On the distribution of the order and index of g(mod p) over residue classes II
• On the distribution of the order and index of g(mod p) over residue classes III
• Divisibility of the Multiplicative Order Modulo Monic Irreducible Polynomials Over Finite Fields