On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)

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dc.contributor.authorBai, Hairong
dc.contributor.authorYuan, Pingzhi
dc.contributor.buuauthorKızıldere, Elif
dc.contributor.buuauthorSoydan, Gökhan
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.tr_TR
dc.contributor.orcid0000-0002-6321-4132tr_TR
dc.contributor.scopusid57204173004tr_TR
dc.contributor.scopusid23566953200tr_TR
dc.date.accessioned2022-12-15T11:09:33Z
dc.date.available2022-12-15T11:09:33Z
dc.date.issued2020-03-30
dc.description.abstractSuppose that n is a positive integer. We show that the only positive integer solutions (n, x, y, z) of the exponential Diophantine equation (n - 1)(x) + (n + 2)(y) = nz, n >= 2, xyz not equal 0, are (3, 2, 1, 2), (3,1, 2, 3). The main tools in the proofs are Baker's theory and Bilu-Hanrot-Voutier's result on primitive divisors of Lucas numbers.en_US
dc.description.sponsorshipNational Natural Science Foundation of China (NSFC) (11671153)en_US
dc.identifier.citationBai, H. vd. (2020). "On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)". Colloquium Mathematicum, 161(2), 239-249.en_US
dc.identifier.endpage249tr_TR
dc.identifier.issn0010-1354
dc.identifier.issn1730-6302
dc.identifier.issue2tr_TR
dc.identifier.scopus2-s2.0-85084753117tr_TR
dc.identifier.startpage239tr_TR
dc.identifier.urihttps://doi.org/10.4064/cm7668-6-2019
dc.identifier.urihttps://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/161/2/113556/on-the-exponential-diophantine-equation-n-1-x-n-2-y-n-z
dc.identifier.urihttp://hdl.handle.net/11452/29912
dc.identifier.volume161tr_TR
dc.identifier.wos000571757800005
dc.indexed.scopusScopusen_US
dc.indexed.wosSCIEen_US
dc.language.isoenen_US
dc.publisherArs Polona-Ruchen_US
dc.relation.collaborationYurt dışıtr_TR
dc.relation.journalColloquium Mathematicumen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergitr_TR
dc.relation.tubitak117f287tr_TR
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectExponential Diophantine equationen_US
dc.subjectPrimitive divisors of Lucas sequencesen_US
dc.subjectJacobi symbolen_US
dc.subjectLower bounds for linear forms in two logarithmsen_US
dc.subjectPrimitive divisorsen_US
dc.subjectLinear-formsen_US
dc.subject2 Logarithmsen_US
dc.subjectConjectureen_US
dc.subjectNumberen_US
dc.subjectLucasen_US
dc.subjectMathematicsen_US
dc.subject.scopusDiophantine Equation; Number; Linear Forms in Logarithmsen_US
dc.subject.wosMathematicsen_US
dc.titleOn the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)en_US
dc.typeArticle
dc.wos.quartileQ4en_US

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