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 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.
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Arnaud Bodin, Pierre Dèbes, Salah Najib, Prime and coprime values of polynomials. Enseign. Math. 66 (2020), no. 1/2, pp. 173–186DOI 10.4171/LEM/66-1/2-9