On the system of Diophantine equations \((m^2 - 1)^r + b^2 = c^2\) and \((m^2 - 1)^x + b^y = c^z\)

DOI10.1016/J.JNT.2014.12.021zbMath1365.11033OpenAlexW2325660201MaRDI QIDQ2344351

Florian Luca, Takafumi Miyazaki

Publication date: 13 May 2015

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.12.021

zbMATH Keywords

exponential Diophantine equationlinear form in logarithms of algebraic numbers

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (1)

An upper bound for the number of solutions of ternary purely exponential Diophantine equations

Cites Work

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• Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples. II
• Exceptional cases of Terai's conjecture on Diophantine equations
• Linear forms in two logarithms and interpolation determinants
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• The shuffle variant of Terai's conjecture on exponential Diophantine equations
• On the system of Diophantine equations a²+b²=(m²+1)^rand a^x+b^y=(m²+1)^z
• An application of a lower bound for linear forms in two logarithms to the Terai–Jeśmanowicz conjecture
• Linear forms in p-adic logarithms and the Diophantine equation formula here
• TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS
• A note on the article by F. Luca ``On the system of Diophantine equations a²+b²=(m²+1)^rand a^x+b^y=(m²+1)^z (Acta Arith. 153 (2012), 373–392)

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