On simultaneous Pell equations \(x^{2}-(a^{2}-1)y^{2}=1\) and \(y^{2}-pz^{2}=1\)

DOI10.1016/j.jnt.2017.08.014zbMath1374.11023OpenAlexW2757586705MaRDI QIDQ1677486

Yunyun Qu

Publication date: 21 November 2017

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.08.014

zbMATH Keywords

Diophantine approximationlinear form in logarithms

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (4)

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

Cites Work

• Complete solutions of the simultaneous Pell equations \(x^2 - 24y^2 = 1\) and \(y^2 - pz^2 = 1\)
• Powers of two as sums of three Fibonacci numbers
• On solutions of the simultaneous {P}ell equations {\(x^2-(a^2-1)y^2=1\)} and {\(y^2-pz^2=1\)}
• Simultaneous Pell equations
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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