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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

irreducible polynomial


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.

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