The Diophantine equation (m2 + n2)x + (2mn)y = (m + n)2z

DOI10.1142/S179304212050089XzbMath1472.11107OpenAlexW3012490107MaRDI QIDQ4970748

Xiao-Hui Yan

Publication date: 7 October 2020

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

Full work available at URL: https://doi.org/10.1142/s179304212050089x

zbMATH Keywords

exponential Diophantine equationJeśmanowicz conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (2)

A Heron triangle and a Diophantine equation ⋮ Construction of an infinite family of elliptic curves of 2-Selmer rank 1 from Heron triangles

Cites Work

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• On Jeśmanowicz' conjecture concerning primitive Pythagorean triples
• Jeśmanowicz' conjecture with Fermat numbers
• On Jeśmanowicz' conjecture concerning primitive Pythagorean triples. II
• Jeśmanowicz' conjecture on exponential Diophantine equations
• A remark on Jeśmanowicz' conjecture
• Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples
• The Diophantine equation \(Ax^ p+By^ q=Cz^ r\).
• The Diophantine equation (bn)^x+(2n)^y=((b+2)n)^z
• JEŚMANOWICZ’ CONJECTURE REVISITED
• THE DIOPHANTINE EQUATION (2am - 1)^x + (2m)^y = (2am + 1)^z
• A note on Jeśmanowicz' conjecture concerning Pythagorean triples
• An application of a lower bound for linear forms in two logarithms to the Terai–Jeśmanowicz conjecture
• Chabauty methods using elliptic curves
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Jeśmanowicz' conjecture and related equations
• JEŚMANOWICZ’ CONJECTURE ON PYTHAGOREAN TRIPLES
• Number Theory

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