Geodesic
Pellans Sequence and Its Diophantine Triples
Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 259 .

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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=S_x, \quad ac+1=S_y \quad bc+1=S_z $ where $a$ are positive integers. Therefore, we extend the order of recurrence sequence for this variant diophantine equations by means of pellans sequence.
DOI : 10.2298/PIM1614259I
Classification : 11D09 11B39
Keywords: Diophantine triples, pell numbers, balancing numbers, pellans sequence 
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Nurettin Irmak; Murat Alp. Pellans Sequence and Its Diophantine Triples. Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 259 . doi : 10.2298/PIM1614259I. http://geodesic.mathdoc.fr/articles/10.2298/PIM1614259I/

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