Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1

DOI10.1090/proc/13802zbMath1420.11060OpenAlexW2613629986MaRDI QIDQ3130820

Mihai Cipu

Publication date: 29 January 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13802

zbMATH Keywords

Pell equationsquartic Diophantine equationsLucas/Lehmer sequences

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Related Items

Complete solutions of the simultaneous Pell equations \((a^2+1)y^2-x^2 = y^2-bz^2 = 1\), On the cubic Pell equation over finite fields, Uniqueness conjecture on simultaneous Pell equations, 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

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