Complete solutions of the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $

AIMS Mathematics ◽

10.3934/math.2021577 ◽

2021 ◽

Vol 6 (9) ◽

pp. 9919-9938

Author(s):

Changsheng Luo ◽

◽

Jiagui Luo

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations ◽

Complete Solutions

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On the number of solutions of simultaneous Pell equations

Acta Arithmetica ◽

10.4064/aa101-3-2 ◽

2002 ◽

Vol 101 (3) ◽

pp. 215-221 ◽

Author(s):

Pingzhi Yuan

Keyword(s):

Number Of Solutions ◽

Pell Equations ◽

Simultaneous Pell Equations

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Common Solutions of Two Simultaneous Pell Equations

Annals of Mathematics ◽

10.2307/1967756 ◽

1922 ◽

Vol 23 (4) ◽

pp. 307 ◽

Author(s):

A. Arwin

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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Solving Families of Simultaneous Pell Equations

Journal of Number Theory ◽

10.1006/jnth.1997.2188 ◽

1997 ◽

Vol 67 (2) ◽

pp. 246-251 ◽

Author(s):

Michael A Bennett

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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A note on the simultaneous Pell equations $$x^2-(a^2-1)y^2=1$$ and $$y^2-bz^2=1$$

Periodica Mathematica Hungarica ◽

10.1007/s10998-020-00334-1 ◽

2020 ◽

Vol 81 (2) ◽

pp. 234-238

Author(s):

Xing-Wang Jiang

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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Explicit formula for the solution of simultaneous Pell equations $x^2-(a^2-1)y^2=1$, $y^2-bz^2=1$

Proceedings of the American Mathematical Society ◽

10.1090/proc/13802 ◽

2017 ◽

Vol 146 (3) ◽

pp. 983-992 ◽

Author(s):

Mihai Cipu

Keyword(s):

Explicit Formula ◽

Pell Equations ◽

Simultaneous Pell Equations

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On the determination of solutions of simultaneous Pell equations $$x^{2}-(a^{2}-1)y^{2}=y^{2}-pz^{2}=1$$ x 2 - ( a 2 - 1 ) y 2 = y 2 - p z 2 = 1

Periodica Mathematica Hungarica ◽

10.1007/s10998-017-0203-2 ◽

2017 ◽

Vol 75 (2) ◽

pp. 336-344

Author(s):

Refik Keskin ◽

Olcay Karaatlı ◽

Zafer Şiar ◽

Ümmügülsüm Öğüt

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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The Qu (2018) Conjectures, The Yang & Fu (2018) Conjectures, The Jiang (2020) Conjecture, The Tao (2016) Conjectures, The Cipu (2007) Conjecture, The Cipu & Mignotte (2007) Conjecture And The Simultaneous Pell Equations x2−(a2−1)y2=1 and y2−pz2=1

SSRN Electronic Journal ◽

10.2139/ssrn.3610352 ◽

2020 ◽

Author(s):

Michael C. I. Nwogugu

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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On two classes of simultaneous Pell equations with no solutions

Mathematics of Computation ◽

10.1090/s0025-5718-99-01048-0 ◽

1999 ◽

Vol 68 (225) ◽

pp. 385-389 ◽

Author(s):

P. G. Walsh

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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Corrigendum to “On two classes of simultaneous Pell equations with no solutions”

Mathematics of Computation ◽

10.1090/mcom/3677 ◽

2021 ◽

pp. 1

Author(s):

P. G. Walsh

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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A note on the simultaneous Pell equations x^2-24y^2=1 and y^2-pz^2=1

Pure Mathematical Sciences ◽

10.12988/pms.2016.51117 ◽

2016 ◽

Vol 5 ◽

pp. 27-32

Author(s):

Liqun Tao

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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