On a variant of Pillai’s problem

DOI10.1142/S1793042117500981zbMath1433.11035arXiv1604.04719MaRDI QIDQ4975307

István Pink, Kwok Chi Chim, Volker Ziegler

Publication date: 4 August 2017

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

Full work available at URL: https://arxiv.org/abs/1604.04719

zbMATH Keywords

Fibonacci sequenceDiophantine equationsPillai's problemTribonacci sequence

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (16)

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Cites Work

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• Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen. (Algebraic points on analytic subgroups of algebraic groups)
• On a problem of Pillai with Fibonacci numbers and powers of 2
• On Some Exponential Equations of S. S. Pillai
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• On a conjecture about repdigits in k-generalized Fibonacci sequences
• Logarithmic forms and group varieties.
• Primary cyclotomic units and a proof of Catalans conjecture
• Linear forms in the logarithms of algebraic numbers
• Linear forms in the logarithms of algebraic numbers (II)
• Linear forms in the logarithms of algebraic numbers (III)
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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