On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers

DOI10.1016/j.jnt.2019.07.006zbMath1447.11025arXiv1803.10434OpenAlexW2970922113WikidataQ114157236 ScholiaQ114157236MaRDI QIDQ2329269

Florian Luca, Mahadi Ddamulira

Publication date: 17 October 2019

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

Full work available at URL: https://arxiv.org/abs/1803.10434

zbMATH Keywords

Pell equationreduction methodgeneralized Fibonacci sequencelinear form in logarithms

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 (10)

Terms of recurrence sequences in the solution sets of generalized Pell equations ⋮ Sums of \(S\)-units in the solution sets of generalized Pell equations ⋮ On the \(X\)-coordinates of Pell equations of the form \(px^2\) ⋮ The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. ⋮ Unnamed Item ⋮ On the \(x\)-coordinates of Pell equations that are sums of two Padovan numbers ⋮ 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

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• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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