Vol. 9, No. 3, 2016

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The irreducibility of polynomials related to a question of Schur

Lenny Jones and Alicia Lamarche

Vol. 9 (2016), No. 3, 453–464
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.

Keywords
irreducible polynomial
Mathematical Subject Classification 2010
Primary: 12E05, 11C08
Milestones
Received: 14 March 2015
Revised: 18 May 2015
Accepted: 17 June 2015
Published: 3 June 2016

Communicated by Kenneth S. Berenhaut
Authors
Lenny Jones
Department of Mathematics
Shippensburg University
Shippensburg, PA 17257-2299
United States
Alicia Lamarche
Department of Mathematics
Shippensburg University
Shippensburg, PA 17257-2299
United States