Publications de l’Institut Mathématique, Nouvelle Série Vol. 100[114], No. 1/1, pp. 259–269 (2016) 

PELLANS SEQUENCE AND ITS DIOPHANTINE TRIPLESNurettin Irmak, Murat AlpDepartment of Mathematics, Art and Science Faculty, Niğde University, Niğde, TurkeyAbstract: We introduce a novel fourth order linear recurrence sequence $\left\{{S}_{n}\right\}$ using the two periodic binary recurrence. We call it “pellans sequence” and then we solve the system $$$$ ab+1=S $$$$ where $a<b<c$ are positive integers. Therefore, we extend the order of recurrence sequence for this variant diophantine equations by means of pellans sequence. Keywords: Diophantine triples; pell numbers; balancing numbers; pellans sequence Classification (MSC2000): 11D09; 11B39 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.
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