A polynomial with a root mod $p$ for every $p$ has a real root

Rodrigo Angelo; Max Wenqiang Xu

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arXiv · 2210.13735

A polynomial with a root mod $p$ for every $p$ has a real root

Rodrigo Angelo·Max Wenqiang Xu

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Abstract

We prove that if a polynomial has a root mod $p$ for every large prime $p$, then it has a real root. As an application, we show that the primes can't be covered by finitely many positive definite binary quadratic forms.

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Rodrigo Angelo, Max Wenqiang Xu. 2022-10-25. A polynomial with a root mod $p$ for every $p$ has a real root. https://arxiv.org/abs/2210.13735

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