Prime and coprime values of polynomials

  • Arnaud Bodin

    Université de Lille, Villeneuve-d’Ascq, France
  • Pierre Dèbes

    Université de Lille, Villeneuve-d'Ascq, France
  • Salah Najib

    Université Sultan Moulay Slimane, Khouribga, Morocco
Prime and coprime values of polynomials cover
Download PDF

A subscription is required to access this article.


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.

Cite this article

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

DOI 10.4171/LEM/66-1/2-9