On primes p for which d divides ordp(g)
Pieter Moree
Abstract
Let Ng(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 Ng(d)(x) be the number of primes p<=x that are in Ng(d). A simple identity for Ng(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.
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