  Let a and b be non-zero rational numbers that are multiplicatively
independent. We study the natural density of the set of primes p for which the
subgroup of the multiplicative group of the finite field with p elements
generated by (a\mod p) contains (b\mod p). It is shown that, under assumption
of the generalized Riemann hypothesis (GRH), this density exists and equals a
positive rational multiple of the universal constant S=\prod_{p
prime}(1-p/(p^3-1)). An explicit value of the density is given under mild
conditions on a and b. This extends and corrects earlier work of P.J. Stephens
(1976). Our result, in combination with earlier work of the second author,
allows us to deduce that any second order linear recurrence with reducible
characteristic polynomial having integer elements, has a positive density of
prime divisors (under GRH).
