The extension of the \(D(-k)\)-triple \(\{1,k,k+1\}\) to a quadruple

DOI10.1007/s10474-022-01216-3OpenAlexW4223604536MaRDI QIDQ2151109

Kouèssi Norbert Adédji, Alan Filipin, Alain S. Togbé

Publication date: 30 June 2022

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-022-01216-3

zbMATH Keywords

Pellian equationhypergeometric methodlinear form in logarithms of algebraic numbersDiophantine \(m\)-tuple

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Cites Work

• On \(k\)-triad sequences
• An absolute bound for the size of Diophantine \(m\)-tuples
• Two-parameter families of uniquely extendable Diophantine triples
• On the Diophantine pair \(\{a,3a\}\)
• The extension of the \(D(-k)\)-pair \(\{k,k+1\}\) to a quadruple
• The extension of the \(D(-k^2)\)-pair \(\left\{k^2, k^2+1\right\}\)
• Linear forms in two logarithms and interpolation determinants II
• Sets in Which xy + k is Always a Square
• Generalization of a problem of Diophantus
• The regularity of Diophantine quadruples
• On the number of extensions of a Diophantine triple
• There is no Diophantine quintuple
• A note on the regularity of the Diophantine pair \protect \lbrace k,4k\pm 4\protect \rbrace
• On the extension of $D(-8k^2)$-pair $\{8k^2, 8k^2+1\}$

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