Publication:
A modular approach to the generalized ramanujan-nagell equation

dc.contributor.authorLe, Maohua
dc.contributor.buuauthorMutlu, Elif Kizildere
dc.contributor.buuauthorSoydan, Gokhan
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.
dc.contributor.orcid0000-0002-7651-7001
dc.contributor.researcheridM-9459-2017
dc.date.accessioned2024-09-17T07:28:19Z
dc.date.available2024-09-17T07:28:19Z
dc.date.issued2022-08-20
dc.description.abstractLet k be a positive integer. In this paper, using the modular approach, we prove that if k & EQUIV; 0 (mod 4), 30 < k < 724 and 2k -1 is an odd prime power, then under the GRH, the equation x2 + (2k -1)y = kz has only one positive integer solution (x, y, z) = (k - 1, 1, 2). The above results solve some difficult cases of Terai's conjecture concerning this equation.(c) 2022 Royal Dutch Mathematical Society (KWG).
dc.identifier.doi10.1016/j.indag.2022.04.005
dc.identifier.endpage1000
dc.identifier.issn0019-3577
dc.identifier.issue5
dc.identifier.startpage992
dc.identifier.urihttps://doi.org/10.1016/j.indag.2022.04.005
dc.identifier.urihttps://hdl.handle.net/11452/44818
dc.identifier.volume33
dc.identifier.wos000849224700006
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherElsevier
dc.relation.bapF-2020/8
dc.relation.journalIndagationes Mathematicae-new Series
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectDiophantine equations
dc.subjectPoints
dc.subjectPolynomial-exponential diophantine equation
dc.subjectElliptic curve
dc.subjectS-integral point
dc.subjectModular approach
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleA modular approach to the generalized ramanujan-nagell equation
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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