Let
and
be nonzero integers such that (except when ). Also let be the set of primes for which for some nonnegative
integer.
Then assuming the generalized Riemann
hypothesis, Stephens (1976) showed that the density of relative to the primes is a rational multiple of
(OEIS A065478), where is the th prime (Finch 2003).
Finch, S. R. "Artin's Constant." §2.4 in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 104-110,
2003.Moree, P. "Approximation of Singular Series and Automata."
Submitted to Manuscripta Math.101, 385-399, 2000.Moree,
P. and Stevenhagen, P. "A Two-Variable Artin Conjecture." J. Number
Th.85, 291-304, 2000.Niklasch, G. "Some Number-Theoretical
Constants." http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml.Sloane,
N. J. A. Sequence A065478 in "The
On-Line Encyclopedia of Integer Sequences."Stephens, P. J.
"Prime Divisor of Second-Order Linear Recurrences, I." J. Number Th.8,
313-332, 1976.
and 
be nonzero integers such that 
(except when 
). Also let 
be the set of primes 
for which 
for some nonnegative
integer 
.
Then assuming the generalized Riemann
hypothesis, Stephens (1976) showed that the density of 
relative to the primes is a rational multiple of
is the 
th 