On the determination of solutions of simultaneous Pell equations x2- (a2- 1) y2= y2- pz2= 1

dc.contributor.author	Keskin, R. and Karaatlı, O. and Şiar, Z. and t, Ü.
dc.date.accessioned	2021-04-08T12:07:45Z
dc.date.available	2021-04-08T12:07:45Z
dc.date.issued	2017
dc.identifier	10.1007/s10998-017-0203-2
dc.identifier.issn	00315303
dc.identifier.uri	https://www.scopus.com/inward/record.uri?eid=2-s2.0-85027509463&doi=10.1007%2fs10998-017-0203-2&partnerID=40&md5=d3f7b2545c34e77299cc17ddee6a7d82
dc.identifier.uri	http://acikerisim.bingol.edu.tr/handle/20.500.12898/4438
dc.description.abstract	In this paper, we consider the simultaneous Pell equations x2-(a2-1)y2=1,y2-pz2=1,where p is prime and a> 1. Assuming the solutions of the Pell equation x2- (a2- 1) y2= 1 are x= xm and y= ym with m≥ 2 , we prove that the system (0.1) has solutions only when m= 2 or m= 3. In the case of m= 3 , we show that p= 2 and give the solutions of (0.1) in terms of Pell and Pell–Lucas sequences. When m= 2 and p≡3(mod4), we determine the values of a, x, y, and z. Lastly, we show that (0.1) has no solutions when p≡1(mod4). © 2017, Akadémiai Kiadó, Budapest, Hungary.
dc.language.iso	English
dc.source	Periodica Mathematica Hungarica
dc.title	On the determination of solutions of simultaneous Pell equations x2- (a2- 1) y2= y2- pz2= 1

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