Powers in recurrence sequences: Pell equations

DOI10.1090/S0002-9947-04-03586-XzbMath1125.11019OpenAlexW2096252136MaRDI QIDQ3155974

Michael A. Bennett

Publication date: 5 January 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03586-x

zbMATH Keywords

Thue equationsmodular formsperfect powersFrey curvesPell sequences

Mathematics Subject Classification ID

Recurrences (11B37) Counting solutions of Diophantine equations (11D45) Higher degree equations; Fermat's equation (11D41)

Related Items (3)

ON PERFECT POWERS IN LUCAS SEQUENCES ⋮ Diophantine equations after Fermat's last theorem ⋮ Powers in Lucas sequences via Galois representations

Cites Work

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• Dimensions of the spaces of cusp forms and newforms on \(\Gamma_0(N)\) and \(\Gamma_1(N)\)
• Pure powers in recurrence sequences and some related diophantine equations
• Polynomial values and almost powers
• Perfect powers in second order linear recurrences
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
• The Diophantine equation $b^2X^4-dY^2=1$
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Ternary Diophantine equations of signature (p, p, 3)
• PRODUCTS OF CONSECUTIVE INTEGERS
• Perfect Pell Powers
• A note on the equation $ax^n - by^n = c$
• On the least solution of Pell’s equation

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