  The Schinzel Hypothesis is a celebrated conjecture in number theory linking
polynomial values and prime numbers. In the same vein we investigate the common
divisors of values $P_1(n),\ldots, P_s(n)$ of several polynomials. We deduce
this coprime version of the Schinzel Hypothesis: under some natural assumption,
coprime polynomials assume coprime values at infinitely many integers.
Consequences include a version "modulo an integer" of the original Schinzel
Hypothesis, with the Goldbach conjecture, again modulo an integer, as a special
case.
