Publication: On the diophantine equation Σj=1k jFjp = Fnq
dc.contributor.author | Nemeth, Laszlo | |
dc.contributor.author | Szalay, Laszlo | |
dc.contributor.buuauthor | Soydan, Gökhan | |
dc.contributor.buuauthor | SOYDAN, GÖKHAN | |
dc.contributor.department | Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı. | |
dc.contributor.researcherid | M-9459-2017 | |
dc.date.accessioned | 2024-11-04T12:54:51Z | |
dc.date.available | 2024-11-04T12:54:51Z | |
dc.date.issued | 2018-01-01 | |
dc.description.abstract | Let 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.doi | 10.5817/AM2018-3-177 | |
dc.identifier.endpage | 188 | |
dc.identifier.issn | 1212-5059 | |
dc.identifier.issue | 3 | |
dc.identifier.startpage | 177 | |
dc.identifier.uri | https://doi.org/10.5817/AM2018-3-177 | |
dc.identifier.uri | https://hdl.handle.net/11452/47407 | |
dc.identifier.volume | 54 | |
dc.identifier.wos | 000441100400005 | |
dc.indexed.wos | WOS.ESCI | |
dc.language.iso | en | |
dc.publisher | Masaryk Univ, Fac Science | |
dc.relation.bap | 2015/23 | |
dc.relation.bap | 2016/9 | |
dc.relation.journal | Archivum Mathematicum | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | |
dc.rights | info:eu-repo/semantics/closedAccess | |
dc.subject | Consecutive fibonacci numbers | |
dc.subject | Powers | |
dc.subject | Sequence | |
dc.subject | Sum | |
dc.subject | Fibonacci sequence | |
dc.subject | Diophantine equation | |
dc.subject | Science & technology | |
dc.subject | Physical sciences | |
dc.subject | Mathematics | |
dc.title | On the diophantine equation Σj=1k jFjp = Fnq | |
dc.type | Article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 356f7af9-3f0f-4c82-8733-d98627634647 | |
relation.isAuthorOfPublication.latestForDiscovery | 356f7af9-3f0f-4c82-8733-d98627634647 |
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