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A family of integer Somos sequences

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dc.contributor.buuauthorGezer, Betül
dc.contributor.buuauthorÇapa, Buse
dc.contributor.buuauthorBizim, Osman
dc.contributor.departmentFen Edebiyat Fakültesi
dc.contributor.departmentMatematik Bölümü
dc.contributor.researcheridAAH-1547-2021
dc.contributor.researcheridAAH-1468-2021
dc.contributor.scopusid24485316600
dc.contributor.scopusid57194222837
dc.contributor.scopusid9245697900
dc.date.accessioned2023-06-08T10:28:13Z
dc.date.available2023-06-08T10:28:13Z
dc.date.issued2016
dc.description.abstractSomos sequences are sequences of rational numbers defined by a bilinear recurrence relation. Remarkably, although the recurrences describing the Somos sequences are rational, some Somos sequences turn out to have only integer terms. In this paper, a family of Somos 4 sequences is given and it is proved that all Somos 4 sequences associated to Tate normal forms with h(-1) - +/- 1 consist entirely of integers for n >= 0. It is also shown that there are infinitely many squares and infinitely many cubes in Somos 4 sequences associated to Tate normal forms.
dc.identifier.citationGezer, B. vd. (2016). "A family of integer Somos sequences". Mathematical Reports, 18(3), 417-435.
dc.identifier.endpage435
dc.identifier.issn1582-3067
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85019293455
dc.identifier.startpage417
dc.identifier.urihttp://hdl.handle.net/11452/32978
dc.identifier.volume18
dc.identifier.wos000383902800011
dc.indexed.wosSCIE
dc.language.isoen
dc.publisherEditura Acad Romane
dc.relation.journalMathematical Reports
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectMathematics
dc.subjectSomos sequences
dc.subjectElliptic curves
dc.subjectTorsion points
dc.subjectElliptic divisibility sequences
dc.subjectLucas sequences
dc.subjectLaurent phenomenon
dc.subjectPerfect powers
dc.subjectSquares
dc.subjectCubes
dc.subjectFibonacci
dc.subjectTorsion
dc.subjectCurves
dc.subject.scopusSymmetry; Discrete Equations; Affine Weyl Groups
dc.subject.wosMathematics
dc.titleA family of integer Somos sequences
dc.typeArticle
dc.wos.quartileQ4
dspace.entity.typePublication
local.contributor.departmentFen Edebiyat Fakültesi/Matematik Bölümü
local.indexed.atScopus
local.indexed.atWOS

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