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

Max Wenqiang Xu; Rodrigo Angelo

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arxiv 2210.13735 v2 pith:GTO25LXF submitted 2022-10-25 math.NT

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

Rodrigo Angelo , Max Wenqiang Xu This is my paper

classification math.NT

keywords rooteverypolynomialrealapplicationbinarycovereddefinite

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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.

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

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