Primes dividing values of a given Polynomial

preprint2022arXivOpen access

Abstract

Let P(x)∈Z[x]P(x) \in \mathbb{Z}[x] be a polynomial. We give an easy and new proof of the fact that the set of primes pp such that p∣P(n)p \mid P(n), for some n∈Zn \in \mathbb{Z}, is infinite. We also get analog of this result for some special domains.

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