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

2022/10/25 by Rodrigo Angelo, Angelo, Rodrigo, Max Wenqiang Xu +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2210.13735

openalex publication_date 2022/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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