The problem of the extension of D(4)-triple {1, b, c}

DOI10.21857/ygjwrcpgoyOpenAlexW4313045826MaRDI QIDQ5041974

Alan Filipin, Kouèssi Norbert Adédji, Alain S. Togbé

Publication date: 18 October 2022

Published in: Rad Hrvatske akademije znanosti i umjetnosti Matematičke znanosti (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21857/ygjwrcpgoy

zbMATH Keywords

Diophantine \(m\)-tuplesreduction methodlinear form in logarithmssystem of Pellian equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Continued fraction calculations (number-theoretic aspects) (11Y65) Linear forms in logarithms; Baker's method (11J86) Approximation to algebraic numbers (11J68)

Related Items

On the \(D(4)\)-pairs \(\{a, ka\}\) with \(k\in \{2,3,6\}\) ⋮ \(D(4)\)-triples with two largest elements in common

Cites Work

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• Extension of a Diophantine triple with the property \(D(4)\)
• Nonexistence of \(D(4)\)-quintuples
• On the size of sets in which \(xy + 4\) is always a square
• Another generalization of a theorem of Baker and Davenport
• 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
• On a family of two-parametric D(4)-triples
• Linear forms in two logarithms and interpolation determinants II
• There are only finitely many Diophantine quintuples
• There is no Diophantine quintuple
• The extension of some D(4)-pairs
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²