Irreducibility of a Polynomial Shifted by a Power of Another Polynomial

Author:

Dubickas Artūras1ORCID

Affiliation:

1. Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

Abstract

In this note, we show that, for any f x and any prime number p , there exists g x for which the polynomial f x g x p is irreducible over . 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 a h x k , where a 0 and k 2 are integers and h x .

Funder

European Social Fund

Publisher

Hindawi Limited

Subject

General Mathematics

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