A polynomial with a root mod $p$ for every $p$ has a real root
Number Theory
2024-06-24 v2
Abstract
We prove that if a polynomial has a root mod for every large prime , 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.
Cite
@article{arxiv.2210.13735,
title = {A polynomial with a root mod $p$ for every $p$ has a real root},
author = {Rodrigo Angelo and Max Wenqiang Xu},
journal= {arXiv preprint arXiv:2210.13735},
year = {2024}
}