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On the diophantine equation (5 pn 2 - 1) x

dc.contributor.authorKızıldere, Elif
dc.contributor.authorSoydan, Gökhan
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.buuauthorKızıldere, Elif
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.orcid0000-0002-6321-4132
dc.contributor.researcheridM-9459-2017
dc.contributor.researcheridGRN-4828-2022
dc.date.accessioned2024-07-05T10:34:06Z
dc.date.available2024-07-05T10:34:06Z
dc.date.issued2020-03-01
dc.description.abstractLet p be a prime number with p > 3, p 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn(2) - 1)(x) + (p(p - 5)n(2) + 1)(y) = (pn)(z) has only the positive integer solution (x; y; z) = (1; 1; 2) where pn +/- 1 (mod 5). As an another result, we show that the Diophantine equation (35n(2) - 1)(x) + (14n(2) + 1)(y) = (7n)(z) has only the positive integer solution (x, y, z) = (1; 1; 2) where n +/- 3 (mod 5) or 5 vertical bar n. On the proofs, we use the properties of Jacobi symbol and Baker's method.
dc.identifier.doi10.5831/HMJ.2020.42.1.139
dc.identifier.eissn2288-6176
dc.identifier.endpage150
dc.identifier.issn1225-293X
dc.identifier.issue1
dc.identifier.startpage139
dc.identifier.urihttps://doi.org/10.5831/HMJ.2020.42.1.139
dc.identifier.urihttp://koreascience.or.kr/article/JAKO202009444381938.page
dc.identifier.urihttps://hdl.handle.net/11452/42971
dc.identifier.volume42
dc.identifier.wos000523592000010
dc.indexed.wosWOS.ESCI
dc.language.isoen
dc.publisherHonam Mathematical Soc
dc.relation.journalHonam Mathematical Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.relation.tubitak117F287
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectLinear-forms
dc.subject2 logarithms
dc.subjectConjecture
dc.subjectExponential diophantine equation
dc.subjectJacobi symbol
dc.subjectBaker's method
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleOn the diophantine equation (5 pn 2 - 1) x
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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