Upper bounds for solutions of an exponential Diophantine equation

DOI10.1216/RMJ-2015-45-1-303zbMath1378.11046MaRDI QIDQ2340846

Takafumi Miyazaki

Publication date: 21 April 2015

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1428412783

zbMATH Keywords

\(abc\)-conjectureexponential Diophantine equationsgeneralized Fermat equations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (7)

A purely exponential Diophantine equation in three unknowns ⋮ On the exceptional solutions of Jeśmanowicz' conjecture ⋮ On the Diophantine equation \(a^x+b^y=(a+2)^z\) ⋮ On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\) ⋮ An upper bound for the number of solutions of ternary purely exponential Diophantine equations ⋮ An exponential Diophantine equation related to powers of three consecutive Fibonacci numbers ⋮ On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m\)

Cites Work

• Fibonacci numbers at most one away from a perfect power
• Partial descent on hyperelliptic curves and the generalized Fermat equation x ³ +y ⁴ +z ⁵ =0
• An application of a lower bound for linear forms in two logarithms to the Terai–Jeśmanowicz conjecture
• Chabauty methods using elliptic curves
• On Fibonacci numbers which are one more than a square.
• Number Theory
• Unsolved problems in number theory
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