Variations on a question concerning the degrees of divisors of x^n-1 J

Title:
Variations on a question concerning the degrees of divisors of x^n-1 J
Authors:
Thompson, Lola
Abstract:
In this paper, we examine a natural question concerning the divisors of the polynomial x n -1: “How often does x n -1 have a divisor of every degree between 1 and n?” In a previous paper, we considered the situation when x n -1 is factored in ℤ[x]. In this paper, we replace ℤ[x] with 𝔽 p [x], where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p.
Citation:
Lola Thompson. 2014."Variations on a question concerning the degrees of divisors of x^n-1 J." Theorie des Nombres Bordeaux 26(1): 253-267.
Publisher:
Universite de Bordeaux I, Centre de Recherces en Mathematiques
DATE ISSUED:
2014
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.5802/jtnb.866
PERMANENT LINK:
http://hdl.handle.net/11282/566832

Full metadata record

DC FieldValue Language
dc.contributor.authorThompson, Lolaen
dc.date.accessioned2015-08-13T10:35:07Zen
dc.date.available2015-08-13T10:35:07Zen
dc.date.issued2014en
dc.identifier.citationLola Thompson. 2014."Variations on a question concerning the degrees of divisors of x^n-1 J." Theorie des Nombres Bordeaux 26(1): 253-267.en
dc.identifier.issn1246-7405en
dc.identifier.urihttp://hdl.handle.net/11282/566832en
dc.description.abstractIn this paper, we examine a natural question concerning the divisors of the polynomial x n -1: “How often does x n -1 have a divisor of every degree between 1 and n?” In a previous paper, we considered the situation when x n -1 is factored in ℤ[x]. In this paper, we replace ℤ[x] with 𝔽 p [x], where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p.en
dc.language.isoen_USen
dc.publisherUniversite de Bordeaux I, Centre de Recherces en Mathematiquesen
dc.identifier.doi10.5802/jtnb.866en
dc.subject.departmentMathematicsen
dc.titleVariations on a question concerning the degrees of divisors of x^n-1 Jen
dc.typeArticleen
dc.identifier.journalTheorie des Nombres Bordeauxen
dc.identifier.volume26en
dc.identifier.issue1en
dc.identifier.startpage253en
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