The diophantine equation x2 + paqb = yq

DOI10.1142/S1793042121500792zbMath1486.11051OpenAlexW3159316006MaRDI QIDQ5155875

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Publication date: 8 October 2021

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

Full work available at URL: https://doi.org/10.1142/s1793042121500792

zbMATH Keywords

exponential Diophantine equationLebesgue-Nagell equation

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Uses Software

• SageMath

Cites Work

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• On the exponential Diophantine equation \(x^2 + 2^a p^b = y^n\)
• On the Diophantine equation \(x^2+5^a\cdot 11^b=y^n\)
• Lucas and Lehmer numbers without primitive divisor
• Existence of primitive divisors of Lucas and Lehmer numbers
• Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation
• ON THE DIOPHANTINE EQUATION x² + 2^a · 5^b = yⁿ
• The diophantine equation x² + C = yⁿ
• A note on the Diophantine equations $x^{2}\pm5^{\alpha}\cdot p^{n}=y^{n}$
• Number Theory