Complete solutions of the simultaneous Pell’s equations x2 − (a2 − 1)y2 = 1 and y2 − pz2 = 1

DOI10.1142/S1793042119500593zbMath1441.11060OpenAlexW2906515987MaRDI QIDQ5380765

Ruiqin Fu, Hai Yang

Publication date: 6 June 2019

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

Full work available at URL: https://doi.org/10.1142/s1793042119500593

zbMATH Keywords

solvability conditionsimultaneous Pell's equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09)

Related Items (3)

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 \(y^2-pz^2=4b^2\)

Cites Work

• Complete solutions of the simultaneous Pell equations \(x^2 - 24y^2 = 1\) and \(y^2 - pz^2 = 1\)
• On the number of solutions to systems of Pell equations
• A note on a theorem of Ljunggren and the diophantine equations \(x^2-kxy^2+y^4=1,4\)
• On simultaneous Pell equations \(x^{2}-(a^{2}-1)y^{2}=1\) and \(y^{2}-pz^{2}=1\)
• On the number of solutions of simultaneous Pell equations
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