Reducible cubic CNS polynomials

Shigeki Akiyama; Horst Brunotte; Attila Pethő

doi:10.1007/s10998-007-4177-y

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 55: Issue 2

Reducible cubic CNS polynomials

Authors: Shigeki Akiyama¹, Horst Brunotte², and Attila Pethő³

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¹ Niigata University Department of Mathematics, Faculty of Science Ikarashi 2-8050 Niigata 950-2181 Japan
² Haus-Endt-Strasse 88 D-40593 Düsseldorf Germany
³ University of Debrecen Department of Computer Science P.O. Box 12 H-4010 Debrecen Hungary

DOI:: https://doi.org/10.1007/s10998-007-4177-y

Page Count:: 177–183

Publication Date:: 01 Nov 2007

Online Publication Date:: 08 Jan 2008

Article Category:: Research Article

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Abstract

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials.