Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 3 (2016), 453-464.

The irreducibility of polynomials related to a question of Schur

Lenny Jones and Alicia Lamarche

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Abstract

In 1908, Schur raised the question of the irreducibility over of polynomials of the form f(x) = (x + a1)(x + a2)(x + am) + c, where the ai are distinct integers and c {1,1}. Since then, many authors have addressed variations and generalizations of this question. In this article, we investigate the irreducibility of f(x) and f(x2), where the integers ai are consecutive terms of an arithmetic progression and c is a nonzero integer.

Article information

Source
Involve, Volume 9, Number 3 (2016), 453-464.

Dates
Received: 14 March 2015
Revised: 18 May 2015
Accepted: 17 June 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371025

Digital Object Identifier
doi:10.2140/involve.2016.9.453

Mathematical Reviews number (MathSciNet)
MR3509338

Zentralblatt MATH identifier
1342.12004

Subjects
Primary: 12E05: Polynomials (irreducibility, etc.) 11C08: Polynomials [See also 13F20]

Keywords
irreducible polynomial

Citation

Jones, Lenny; Lamarche, Alicia. The irreducibility of polynomials related to a question of Schur. Involve 9 (2016), no. 3, 453--464. doi:10.2140/involve.2016.9.453. https://projecteuclid.org/euclid.involve/1511371025


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