Complete solutions of the simultaneous Pell equations \(x^2 - 24y^2 = 1\) and \(y^2 - pz^2 = 1\)

DOI10.1016/j.jnt.2014.07.009zbMath1311.11020OpenAlexW115214372MaRDI QIDQ472822

Xiaochuan Ai, Silan Zhang, Hao Hu, Jian-Hua Chen

Publication date: 20 November 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.07.009

zbMATH Keywords

quadratic Diophantine equationsPell equationsimultaneous Pell equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09)

Related Items (9)

On simultaneous Pell equations \(x^{2}-(a^{2}-1)y^{2}=1\) and \(y^{2}-pz^{2}=1\) ⋮ Complete solutions of the simultaneous Pell equations \((a^2+1)y^2-x^2 = y^2-bz^2 = 1\) ⋮ On solutions of the simultaneous {P}ell equations {\(x^2-(a^2-1)y^2=1\)} and {\(y^2-pz^2=1\)} ⋮ On the determination of solutions of simultaneous Pell equations \(x^2 - (a^2 - 1) y^2 = y^2 - pz^2 = 1\) ⋮ Complete solutions of the simultaneous Pell’s equations x2 − (a2 − 1)y2 = 1 and y2 − pz2 = 1 ⋮ A note on the simultaneous Pell equations \(x^2-(a^2-1)y^2=1\) and \(y^2-bz^2=1\) ⋮ On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12 ⋮ On the system of Pell equations \(x^2-(a^2b^2 {\pm } a)y^2=1\) and \(y^2-pz^2=4b^2\) ⋮ Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1

Cites Work

• On the number of solutions to systems of Pell equations
• The Diophantine equation x⁴ - Dy² = 1, II
• On the number of solutions of $x^2-4m(m+1)y^2=y^2-bz^2=1$
• A note on the diophantine equation a²x⁴-By²=1
• Simultaneous Pell equations
• On the number of solutions of simultaneous Pell equations

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