On \(D(-1)\)-triples \(\{1,4p^2+1,1-p\}\) in the ring \(\mathbb{Z}[\sqrt{-p}]\) with a prime \(p\)

DOI10.1007/s10998-021-00435-5OpenAlexW4205734444WikidataQ114224912 ScholiaQ114224912MaRDI QIDQ2678431

Alan Filipin, Mirela Jukić, Ivan Soldo

Publication date: 23 January 2023

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

Full work available at URL: https://doi.org/10.1007/s10998-021-00435-5

zbMATH Keywords

quadratic fieldlinear form in logarithmssimultaneous Pellian equationsDiophantine tuples

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Linear forms in logarithms; Baker's method (11J86)

Cites Work

• \(D(-1)\)-triples of the form \(\{1,b,c\}\) in the ring \(\mathbb Z[\sqrt{-t}\), \(t>0\)]
• On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension
• On the family of Diophantine triples \(\{k+1,4k,9k+3\}\)
• Linear forms in two logarithms and interpolation determinants
• A Pellian equation with primes and applications to \(D(-1)\)-quadruples
• On the extensibility of \(D(-1)\)-pairs containing Fermat primes
• The extensibility of the \(D(\pm k)\)-triple \(\{k\mp 1,k, 4k\mp 1\}\)
• THE NON-EXTENDIBILITY OF SOME PARAMETRIC FAMILIES OF D(-1)-TRIPLES
• On the extensibility of D(−1)-triples {1, b, c} in the ring \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \(\mathbb{Z}\left[ {\sqrt { - t} } \right\) \end{document}, t > 0]
• Logarithmic forms and group varieties.
• There is no Diophantine quintuple
• On the size of Diophantine m-tuples in imaginary quadratic number rings
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
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