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arXiv · 2206.13466

On polynomials with roots modulo almost all primes

Christian Elsholtz·Benjamin Klahn·Marc Technau
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Abstract

Call a monic integer polynomial exceptional if it has a root modulo all but a finite number of primes, but does not have an integer root. We classify all irreducible monic integer polynomials $h$ for which there is an irreducible monic quadratic $g$ such that the product $gh$ is exceptional. We construct exceptional polynomials with all factors of the form $X^{p}-b$, $p$ prime and $b$ square free.

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Christian Elsholtz, Benjamin Klahn, Marc Technau. 2022-06-27. On polynomials with roots modulo almost all primes. https://doi.org/10.4064/aa220407-9-7

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