A modular approach to the generalized Ramanujan-Nagell equation

DOI10.1016/j.indag.2022.04.005zbMath1502.11039arXiv2111.05626OpenAlexW3211471107WikidataQ113872387 ScholiaQ113872387MaRDI QIDQ2166103

Gökhan Soydan, Elif Kızıldere Mutlu, Maohua Le

Publication date: 23 August 2022

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.05626

zbMATH Keywords

elliptic curvemodular approach\(S\)-integral pointpolynomial-exponential Diophantine equation

Mathematics Subject Classification ID

Elliptic curves (14H52) Exponential Diophantine equations (11D61)

Cites Work

• Unnamed Item
• The \(L\)-functions and Modular Forms Database project
• Heegner points and derivatives of \(L\)-series
• The Magma algebra system. I: The user language
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
• On the generalized Ramanujan-Nagell equation \(x^2+(2c-1)^m=c^n\)
• The Generalized Fermat Equation
• Generalized Fermat equations: A miscellany
• Sums of two $S$-units via Frey-Hellegouarch curves
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• A NOTE ON THE DIOPHANTINE EQUATION
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• Computing all S-integral points on elliptic curves
• A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation
• Quelques résultats sur les équations ax^p + by^p = cz²
• A NOTE ON THE DIOPHANTINE EQUATION
• Number Theory

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