A Divisor problem for polynomials

Benjamin Klahn

doi:10.4064/aa200528-21-4

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arXiv · 2202.02100

A Divisor problem for polynomials

Benjamin Klahn

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Abstract

We characterize all monic polynomials $f(x) \in \mathbb{Z}[x]$ that have the property that \[f(p) \mid f(p^{p}),~\text{for all sufficiently large primes }p \geq N(f). \] We also give necessary conditions and a sufficient condition for monic polynomials $f(x) \in \mathbb{Z}[x]$ to satisfy $f(p) \mid f(p^{p})$ for all primes $p$.

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Benjamin Klahn. 2022-02-04. A Divisor problem for polynomials. https://doi.org/10.4064/aa200528-21-4

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