On the number of solutions of simultaneous Pell equations II

Michael A. Bennett; Mihai Cipu; Maurice Mignotte; Ryotaro Okazaki

doi:10.4064/aa122-4-4

On the number of solutions of simultaneous Pell equations II

Acta Arithmetica ◽

10.4064/aa122-4-4 ◽

2006 ◽

Vol 122 (4) ◽

pp. 407-417 ◽

Cited By ~ 9

Author(s):

Michael A. Bennett ◽

Mihai Cipu ◽

Maurice Mignotte ◽

Ryotaro Okazaki

Keyword(s):

Number Of Solutions ◽

Pell Equations ◽

Simultaneous Pell Equations

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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 ◽

Cited By ~ 4

Author(s):

Pingzhi Yuan

Keyword(s):

Number Of Solutions ◽

Pell Equations ◽

Simultaneous Pell Equations

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On the number of solutions of simultaneous Pell equations

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.1998.049 ◽

1998 ◽

Vol 1998 (498) ◽

pp. 173-199 ◽

Cited By ~ 26

Author(s):

Michael A. Bennett

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 ◽

Cited By ~ 1

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 ◽

Cited By ~ 5

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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On the number of solutions to systems of Pell equations

Journal of Number Theory ◽

10.1016/j.jnt.2006.09.016 ◽

2007 ◽

Vol 125 (2) ◽

pp. 356-392 ◽

Cited By ~ 13

Author(s):

Mihai Cipu ◽

Maurice Mignotte

Keyword(s):

Number Of Solutions ◽

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 ◽

Cited By ~ 2

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 ◽

Cited By ~ 2

Author(s):

P. G. Walsh

Keyword(s):

Pell Equations ◽

Simultaneous Pell Equations

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