On the \(D(4)\)-pairs \(\{a, ka\}\) with \(k\in \{2,3,6\}\)

DOI10.3336/GM.58.1.03arXiv2206.12842MaRDI QIDQ6187493

Kouèssi Norbert Adédji, Alain S. Togbé, Alan Filipin, Marija Bliznac Trebješanin

Publication date: 31 January 2024

Published in: Glasnik Matematicki (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.12842

zbMATH Keywords

Diophantine \(m\)-tuplesreduction methodlinear form in logarithmsPellian equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Linear forms in logarithms; Baker's method (11J86) Approximation to algebraic numbers (11J68)

Cites Work

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• Extension of a Diophantine triple with the property \(D(4)\)
• There does not exist a \(D(4)\)-sextuple
• On the Diophantine pair \(\{a,3a\}\)
• On the size of sets in which \(xy + 4\) is always a square
• The extensibility of Diophantine pairs \(\{k - 1,k+1\}\)
• Fibonacci numbers and sets with the property \(D(4)\)
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Logarithmic forms and group varieties.
• The problem of the extension of D(4)-triple {1, b, c}

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