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A polynomial with a root mod $p$ for every $p$ has a real root
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classification
math.NT
keywords
rooteverypolynomialrealapplicationbinarycovereddefinite
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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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