Irreducibility of a Polynomial Shifted by a Power of Another Polynomial

Artūras Dubickas and Marco Fontana

Journal of Mathematics, 2020, vol. 2020, 1-4

Abstract: In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the polynomial fx−gxp is irreducible over ℚ. For composite p≥2, this assertion is not true in general. However, it holds for any integer p≥2 if f is not of the form ahxk, where a≠0 and k≥2 are integers and h∈ℤx.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8869499

DOI: 10.1155/2020/8869499

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