On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3

DOI10.1142/S1793042120500876zbMath1446.11025arXiv1905.01015OpenAlexW3102603879WikidataQ114071947 ScholiaQ114071947MaRDI QIDQ3303493

Florian Luca, Mahadi Ddamulira

Publication date: 11 August 2020

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

Full work available at URL: https://arxiv.org/abs/1905.01015

zbMATH Keywords

linear forms in logarithmsBaker's methodgeneralized Fibonacci numbersPillai's problem

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (8)

On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers ⋮ On a variant of Pillai's problem involving \(S\)-units and Fibonacci numbers ⋮ On a variant of Pillai's problem with factorials and \(S\)-units ⋮ On the Diophantine equation 𝑈_{𝑛}-𝑏^{𝑚}=𝑐 ⋮ On Pillai’s problem with X-coordinates of Pell equations and powers of 2 II ⋮ k-generalized Fibonacci numbers which are concatenations of two repdigits ⋮ Unnamed Item ⋮ On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3

Cites Work

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• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• The equation 2^{𝑥}-3^{𝑦}=𝑑

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