On the \(x\)-coordinates of Pell equations which are products of two Fibonacci numbers

DOI10.1016/j.jnt.2019.03.011zbMath1420.11061OpenAlexW2936691243WikidataQ114157255 ScholiaQ114157255MaRDI QIDQ2312898

Bir Kafle, László Szalay, Amanda Montejano, Florian Luca, Alain S. Togbé

Publication date: 18 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2019.03.011

zbMATH Keywords

linear forms in logarithmsPell equation

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (6)

Terms of recurrence sequences in the solution sets of generalized Pell equations ⋮ Unnamed Item ⋮ Linear combinations of prime powers in \(X\)-coordinates of Pell equations ⋮ An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and \(x\)-coordinates of Pell equations ⋮ On the $x-$coordinates of Pell equations which are sums of two Padovan numbers ⋮ \(X\)-coordinates of Pell equations in various sequences

Cites Work

• Linear forms in two logarithms and interpolation determinants
• 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
• Unnamed Item

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