On solutions of the simultaneous Pell equations and x(2) - (a(2)-1) y(2)=1 and y(2) - pz(2)=1

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dc.contributor.authorIrmak, Nurettin
dc.date.accessioned2019-08-01T13:38:39Z
dc.date.available2019-08-01T13:38:39Z
dc.date.issued2016
dc.departmentNiğde ÖHÜ
dc.description.abstractLet be an integer and p prime number. It is well-known that the solutions of the Pell equation have recurrence relations. For the simultaneous Pell equations x(2) - (a(2) - 1) y(2) = 1 y(2) - pz(2) = 1 assume that and . In this paper, we show that if is an odd integer, then there is no positive solution to the system. Moreover, we find the solutions completely for in the cases when is even integer and m = 1.
dc.identifier.doi10.1007/s10998-016-0137-0
dc.identifier.endpage136
dc.identifier.issn0031-5303
dc.identifier.issn1588-2829
dc.identifier.issue1
dc.identifier.scopus2-s2.0-84964430243
dc.identifier.scopusqualityQ2
dc.identifier.startpage130
dc.identifier.urihttps://dx.doi.org/10.1007/s10998-016-0137-0
dc.identifier.urihttps://hdl.handle.net/11480/3583
dc.identifier.volume73
dc.identifier.wosWOS:000380694300011
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorIrmak, Nurettin
dc.language.isoen
dc.publisherSPRINGER
dc.relation.ispartofPeriodica Mathematica Hungarica
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectDiophantine equation
dc.subjectPell equation
dc.subjectRecurrence
dc.titleOn solutions of the simultaneous Pell equations and x(2) - (a(2)-1) y(2)=1 and y(2) - pz(2)=1
dc.typeArticle

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