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arXiv · 2002.02292

Prime and coprime values of polynomials

Arnaud Bodin·Pierre Dèbes·Salah Najib
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Abstract

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.

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Arnaud Bodin, Pierre Dèbes, Salah Najib. 2020-02-06. Prime and coprime values of polynomials. https://arxiv.org/abs/2002.02292

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