A complete determination of Rabinowitsch polynomials
type: Item
instance of: scholarly article
title: A complete determination of Rabinowitsch polynomials
zbMATH Open document ID: 1290.11145
author: Dongho Byeon
author: Jungyun Lee
published in: Journal of Number Theory
publication date: 2011-05-23T00:00:00Z
review text: Let \(m\) be a positive integer. A Rabinowitsch polynomial is of the form \(f_m(x)=x^2+x-m\), if for \(s=\sqrt{m}\) and consecutive integers \(x=x_0,x_0+1,\ldots, x_0 + s-1\), \(| f_m(x)|\) is either \(1\) or prime. The authors establish that there are exactly fourteen Rabinowitsch polynomials \(f_m(x)\). They fail to reference the deeply related paper by this reviewer: [Int. J. Math. Math. Sci. 2009, Article ID 819068, 14 p. (2009; Zbl 1290.11151)]. Nevertheless their paper is well-written and establishes the closure of another area of this topic.
reviewed by: Richard A. Mollin
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 5899192
zbMATH Keywords: Rabinowitsch polynomial
zbMATH Keywords: prime-producing polynomial
zbMATH Keywords: real quadratic field
MaRDI profile type: Publication
full work available at URL: j.jnt.2011.02.009
OpenAlex ID: W2006315979
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DOI: 10.1016/J.JNT.2011.02.009
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description: scientific article; zbMATH DE number 5899192