Publication:
Resolution of the equation (3 x 1-1)(3x2-1) = (5y1-1)(5y2-1)

dc.contributor.authorLiptai, Kalman
dc.contributor.authorNemeth, Laszlo
dc.contributor.authorSoydan, Gökhan
dc.contributor.authorSzalay, Laszlo
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.orcid0000-0002-6321-4132
dc.contributor.researcheridM-9459-2017
dc.date.accessioned2024-07-26T10:16:14Z
dc.date.available2024-07-26T10:16:14Z
dc.date.issued2020-08-01
dc.description.abstractConsider the diophantine equation (3(x1) - 1)(3(x2) - 1) = (5(y1) - 1)(5(y2) - 1) in positive integers x(1) <= x(2) and y(1) <= y(2). Each side of the equation is a product of two terms of a given binary recurrence. We prove that the only solution to the title equation is (x(1), x(2), y(1), y(2)) = (1, 2, 1, 1). The main novelty of our result is that we allow products of two terms on both sides.
dc.description.sponsorshipOrszagos Tudomanyos Kutatasi Alapprogramok (OTKA) - 128088 - EFOP-3.6.1-16-2016-00018
dc.identifier.doi10.1216/rmj.2020.50.1425
dc.identifier.eissn1945-3795
dc.identifier.endpage1433
dc.identifier.issn0035-7596
dc.identifier.issue4
dc.identifier.startpage1425
dc.identifier.urihttps://doi.org/10.1216/rmj.2020.50.1425
dc.identifier.urihttps://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-50/issue-4/Resolution-of-the-equation-3x_1-13x_2-15y_1-15y_2-1/10.1216/rmj.2020.50.1425.short
dc.identifier.urihttps://arxiv.org/pdf/2001.09717
dc.identifier.urihttps://hdl.handle.net/11452/43472
dc.identifier.volume50
dc.identifier.wos000576337600017
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherRocky Mt Math Consortium
dc.relation.journalRocky Mountain Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectFibonacci
dc.subjectNumbers
dc.subjectExponential diophantine equation
dc.subjectLinear recurrence
dc.subjectBaker method
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleResolution of the equation (3 x 1-1)(3x2-1) = (5y1-1)(5y2-1)
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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