On the determination of solutions of simultaneous Pell equations x(2) - (a(2)-1) y(2) = y(2) - pz(2)=1

Keskin, Refik; Karaatlı, Olcay; Zafer Siar; Ummugulsum Ogut

dc.contributor.authors	Keskin, R; Karaatli, O; Siar, Z; Ogut, U;
dc.date.accessioned	2020-01-17T08:21:42Z
dc.date.available	2020-01-17T08:21:42Z
dc.date.issued	2017
dc.identifier.citation	Keskin, R; Karaatli, O; Siar, Z; Ogut, U; (2017). On the determination of solutions of simultaneous Pell equations x(2) - (a(2)-1) y(2) = y(2) - pz(2)=1. PERIODICA MATHEMATICA HUNGARICA, 75, 344-336
dc.identifier.issn	0031-5303
dc.identifier.uri	https://hdl.handle.net/20.500.12619/6093
dc.identifier.uri	https://doi.org/10.1007/s10998-017-0203-2
dc.description.abstract	where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 are x = x(m) and y = y(m) 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(mod 4), we determine the values of a, x, y, and z. Lastly, we show that (0.1) has no solutions when p = 1(mod 4).
dc.language	English
dc.publisher	SPRINGER
dc.subject	Mathematics
dc.title	On the determination of solutions of simultaneous Pell equations x(2) - (a(2)-1) y(2) = y(2) - pz(2)=1
dc.type	Article
dc.identifier.volume	75
dc.identifier.startpage	336
dc.identifier.endpage	344
dc.contributor.department	Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.saüauthor	Keskin, Refik
dc.contributor.saüauthor	Karaatlı, Olcay
dc.relation.journal	PERIODICA MATHEMATICA HUNGARICA
dc.identifier.wos	WOS:000414229100023
dc.identifier.doi	10.1007/s10998-017-0203-2
dc.identifier.eissn	1588-2829
dc.contributor.author	Keskin, Refik
dc.contributor.author	Karaatlı, Olcay
dc.contributor.author	Zafer Siar
dc.contributor.author	Ummugulsum Ogut