On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12

DOI10.1142/S1793042121500731zbMath1483.11054OpenAlexW3159294845MaRDI QIDQ5155868

Ruiqin Fu, Hai Yang

Publication date: 8 October 2021

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

Full work available at URL: https://doi.org/10.1142/s1793042121500731

zbMATH Keywords

solvabilitysimultaneous Pell equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09)

Related Items (1)

On the cubic Pell equation over finite fields

Cites Work

• Complete solutions of the simultaneous Pell equations \(x^2 - 24y^2 = 1\) and \(y^2 - pz^2 = 1\)
• On simultaneous Pell equations \(x^{2}-(a^{2}-1)y^{2}=1\) and \(y^{2}-pz^{2}=1\)
• 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 \(x^2 - (a^2 - 1) y^2 = y^2 - pz^2 = 1\)
• Squares in Lehmer sequences and some Diophantine applications
• The Diophantine equation x⁴ - Dy² = 1, II
• Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1
• Squares in Lehmer sequences and the Diophantine equation Ax⁴-By²=2
• The Diophantine equation aX 4 – bY 2 = 1
• The Diophantine equation $b^2X^4-dY^2=1$
• On the number of solutions of $x^2-4m(m+1)y^2=y^2-bz^2=1$
• Complete solutions of the simultaneous Pell’s equations x2 − (a2 − 1)y2 = 1 and y2 − pz2 = 1
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