On the X-coordinates of Pell equations X2 − dY2 = ±1 as difference of two Fibonacci numbers

DOI10.1142/s1793042124500258OpenAlexW4387642018MaRDI QIDQ6193634

Carlos Alexis Gómez Ruiz, Alain S. Togbé, Salah Eddine Rihane

Publication date: 18 March 2024

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

Full work available at URL: https://doi.org/10.1142/s1793042124500258

zbMATH Keywords

Fibonacci numberslinear forms in logarithmsPell equationreduction method

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Cites Work

• Unnamed Item
• Unnamed Item
• Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations
• 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
• On $X$-coordinates of Pell equations which are repdigits
• On the $x$-coordinates of Pell equations which are rep-digits
• On the $x$-coordinates of Pell equations which are Fibonacci numbers
• On the $X$-coordinates of Pell equations which are Tribonacci numbers
• On the $x$-coordinates of Pell equations which are Fibonacci numbers II
• The X -coordinates of Pell equations and Padovan numbers

This page was built for publication: On the X-coordinates of Pell equations X2 − dY2 = ±1 as difference of two Fibonacci numbers