A divisor problem for polynomials
Volume 200 / 2021
Acta Arithmetica 200 (2021), 111-118
MSC: 11A07, 11C08, 11T06.
DOI: 10.4064/aa200528-21-4
Published online: 11 August 2021
Abstract
We characterize all monic polynomials $f(x) \in \mathbb {Z}[x]$ that have the property that \[f(p) \,|\, f(p^{p}) \quad \ \text {for all sufficiently large primes }p \geq N(f). \] We also give necessary conditions and a sufficient condition for monic polynomials $f(x) \in \mathbb {Z}[x]$ to satisfy $f(p) \,|\, f(p^{p})$ for all primes $p$.
