Publication:
On the diophantine equation Σj=1k jFjp = Fnq

dc.contributor.authorNemeth, Laszlo
dc.contributor.authorSzalay, Laszlo
dc.contributor.buuauthorSoydan, Gökhan
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.
dc.contributor.researcheridM-9459-2017
dc.date.accessioned2024-11-04T12:54:51Z
dc.date.available2024-11-04T12:54:51Z
dc.date.issued2018-01-01
dc.description.abstractLet F-n denote the nth term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation F-1(p) + 2F(2)(p) + . . . + kF(k)(p) = F-n(q) in the positive integers k and n, where p and q are given positive integers. A complete solution is given if the exponents are included in the set {1, 2}. Based on the specific cases we could solve, and a computer search with p, q, k <= 100 we conjecture that beside the trivial solutions only F-8 = F-1 + 2F(2 )+ 3F(3 )+ 4F(4), F-4(2 )= F-1 + 2F(2) + 3F(3), and F-4(3) = F-1(3)+ 2F(2)(3 )+ 3F(3)(3) satisfy the title equation.
dc.identifier.doi10.5817/AM2018-3-177
dc.identifier.endpage188
dc.identifier.issn1212-5059
dc.identifier.issue3
dc.identifier.startpage177
dc.identifier.urihttps://doi.org/10.5817/AM2018-3-177
dc.identifier.urihttps://hdl.handle.net/11452/47407
dc.identifier.volume54
dc.identifier.wos000441100400005
dc.indexed.wosWOS.ESCI
dc.language.isoen
dc.publisherMasaryk Univ, Fac Science
dc.relation.bap2015/23
dc.relation.bap2016/9
dc.relation.journalArchivum Mathematicum
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectConsecutive fibonacci numbers
dc.subjectPowers
dc.subjectSequence
dc.subjectSum
dc.subjectFibonacci sequence
dc.subjectDiophantine equation
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleOn the diophantine equation Σj=1k jFjp = Fnq
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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