  The Schinzel Hypothesis is a conjecture about irreducible polynomials in one
variable over the integers: under some standard condition, they should assume
infinitely many prime values at integers. We consider a relative version: if
the polynomials are relatively prime and no prime number divides all their
values at integers, then they assume relatively prime values at at least one
integer. We extend the question to all integral domains and prove it for a
number of them: PIDs, UFDs containing an infinite field, polynomial rings over
a UFD. Applications include a new "integral" version of the Hilbert
Irreducibility Theorem, for which the irreducibility conclusion is over the
ring.
