A GENERALIZATION OF THE RAMANUJAN–NAGELL EQUATION

DOI10.1017/S0017089518000344zbMath1477.11061arXiv1712.02199OpenAlexW2962931060MaRDI QIDQ5229050

Tomohiro Yamada

Publication date: 13 August 2019

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.02199

zbMATH Keywords

hypergeometric functiongeneralized Ramanujan-Nagell equation

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61)

Cites Work

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• A note on the number of solutions of the generalized Ramanujan-Nagell equation \(D_ 1x^ 2+D_ 2=4p^ n\)
• The diophantine equation \(x^2+7=2^n\)
• On equations in S-units and the Thue-Mahler equation
• On the diophantine equation \(x^ 2+D=4p^ n\)
• The diophantine equation \(x^ 2=4q^ n-4q+1\)
• Diophantine equation \(x^2+2^m=y^n\)
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• On the Diophantine equation \(x^2+D^m=p^n\)
• On the number of solutions of the generalized Ramanujan-Nagell equation
• Existence of primitive divisors of Lucas and Lehmer numbers
• On the Diophantine equation x ² + C= yⁿ for C = 2 ^a 3 ^b 17 ^c and C = 2 ^a 13 ^b 17 ^c
• On the diophantine equation $D₁x² + D₂ = 2^{n+2}$
• Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation
• On the generalized Ramanujan-Nagell equation I
• On the generalized Ramanujan-Nagell equation, II
• On the diophantine equation $(x^3-1)/(x-1)=(y^n-1)/(y-1)$
• The diophantine equation x² + C = yⁿ
• The Diophantine equation 2𝑥²+1=3ⁿ
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• On some exponential Diophantine equations