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

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Nurettin Irmak, Murat Alp

Department of Mathematics, Art and Science Faculty, Niğde University, Niğde, Turkey

Abstract: We introduce a novel fourth order linear recurrence sequence {S n } using the two periodic binary recurrence. We call it “pellans sequence” and then we solve the system

ab+1=Sx,    ac+1=Sy    bc+1=Sz

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

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

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© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition