Simultaneous integer sequences and solving the pell equation
| dc.contributor.author | Özkoç, Arzu | |
| dc.date.accessioned | 2020-04-30T13:33:22Z | |
| dc.date.available | 2020-04-30T13:33:22Z | |
| dc.date.issued | 2016 | |
| dc.department | DÜ, Fen-Edebiyat Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | Let k ? 1 be a fixed integer. In this work, we set two simultaneous integer sequences defined by Xn = (4k2 + 1)Xn-1 + (4k2 + 1)Xn-2 - Xn-3 and Yn = (4k2 + 1)Yn-1 + (4k2 + 1)Yn-2 - Yn-3 for n ? 3 with initial terms X0 = 1, X1 = 2k2 +1, X2 = 8k4 + 8k2 +1 and Y0 = 0, Y1 = 2k, Y2 = 8k3 + 4k and derived some algebraic identities on them. Further, we are able to determine all integer solutions of the Pell equation x2 - (k2 + 1)y2 = 1 as (xn,yn) = (Xn, Yn) for every n ? 1. © 2016, Jangjeon Mathematical Society. All rights reserved. | en_US |
| dc.identifier.endpage | 275 | en_US |
| dc.identifier.issn | 1229-3067 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.scopusquality | N/A | en_US |
| dc.identifier.startpage | 263 | en_US |
| dc.identifier.uri | https://hdl.handle.net/20.500.12684/621 | |
| dc.identifier.volume | 26 | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Jangjeon Mathematical Society | en_US |
| dc.relation.ispartof | Advanced Studies in Contemporary Mathematics (Kyungshang) | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Binary linear recurrences; Continued fraction; Pell equation; Simultaneous integer sequences | en_US |
| dc.title | Simultaneous integer sequences and solving the pell equation | en_US |
| dc.type | Article | en_US |
