On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\)

DOI10.11650/tjm/220303zbMath1497.11083OpenAlexW4220855956WikidataQ115520531 ScholiaQ115520531MaRDI QIDQ2167797

Florian Luca, Jhonny C. Gómez, Carlos Alexis Gómez Ruiz

Publication date: 31 August 2022

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume-26/issue-4/On-the-Exponential-Diophantine-Equation-F_n1x-F_n-1x/10.11650/tjm/220303.full

zbMATH Keywords

exponential Diophantine equationFibonacci numbersreduction methodlinear form in logarithms

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Diophantine equation \(F_n^x+F_{n+1}^x=F_m^y\)
• On the sum of powers of two consecutive Fibonacci numbers
• Modular elliptic curves and Fermat's Last Theorem
• On the sum of powers of terms of a linear recurrence sequence
• On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m\)
• On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
• An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers
• Upper bounds for solutions of an exponential Diophantine equation
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers
• Primary cyclotomic units and a proof of Catalans conjecture
• Problems in Algebraic Number Theory
• An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers
• On the exponential Diophantine equation Pxn+Pxn+1=Pm
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• On the sum of squares of consecutive $k$-bonacci numbers which are $l$-bonacci numbers
• Number Theory

This page was built for publication: On the exponential Diophantine equation \(F_{n+1}^x - F_{n-1}^x = F_m^y\)