Nonnegative integer solutions of the equationFn

DOI10.3906/mat-1810-83zbMath1455.11054OpenAlexW2947388575WikidataQ127761240 ScholiaQ127761240MaRDI QIDQ5229829

Fatih Erduvan, Refik Keskin

Publication date: 19 August 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1810-83

zbMATH Keywords

Fibonacci numberslinear forms in logarithmsDiophantine equation

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)

Related Items (5)

On the nonnegative integer solutions to the equation \(F_n \pm F_m = y^a\) ⋮ ON SOLUTIONS OF THE DIOPHANTINE EQUATION Fn1 + Fn2 + Fn3 + Fn4 = 2^a ⋮ On the nonnegative integer solutions of the equation F_n ± F_m = y^a ⋮ On solutions of the Diophantine equation \(F_n-F_m=3^a\) ⋮ Mersenne numbers as a difference of two Lucas numbers

Cites Work

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• Effective resolution of Diophantine equations of the form \(u_n+u_m=w p_1^{z_1} \dotsm p_s^{z_s}\)
• On perfect powers that are sums of two Fibonacci numbers
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Linear combinations of prime powers in binary recurrence sequences
• A short history of the Fibonacci and golden numbers with their applications
• On the Diophantine equation $F_{n}-F_{m}=2^{a}$
• On The diophantine equationFn+F_m=2^a
• On Diophantine equations involving sums of Fibonacci numbers and powers of $2$
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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