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k-Diophantine m-tuples in finite fields (Q5881035)

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scientific article; zbMATH DE number 7661280

Language	Label	Description	Also known as
English	k-Diophantine m-tuples in finite fields	scientific article; zbMATH DE number 7661280

Statements

scholarly article

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k-Diophantine m-tuples in finite fields (English)

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Trajan Hammonds

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Steven J. Miller

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International Journal of Number Theory

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publication date

9 March 2023

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full work available at URL

https://arxiv.org/abs/2201.06232

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zbMATH Keywords

character sums

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Diophantine tuples

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elliptic curves

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finite fields

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MaRDI profile type

MaRDI publication profile

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THE EQUATIONS 3<i>x</i><sup>2</sup>−2 = <i>y</i><sup>2</sup> AND 8<i>x</i><sup>2</sup>−7 = <i>z</i><sup>2</sup>

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Nonexistence of \(D(4)\)-quintuples

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There is no Diophantine D(−1)$D(-1)$‐quadruple

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There are only finitely many Diophantine quintuples

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Diophantine \(m\)-tuples and elliptic curves

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Effective solution of the D(-1)-quadruple conjecture

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COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER

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Diophantine \(m\)-tuples in finite fields and modular forms

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There Are Infinitely Many Rational Diophantine Sextuples

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Diophantine quadruples in \(\mathbb {Z}[\sqrt {4k+3}]\)

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A diophantine problem in ℤ[1 + \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} \(\sqrt d\) \end{document})/2]

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Some rational Diophantine sextuples

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There is no Diophantine quintuple

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The Diophantine Equation <i>n</i> ! + 1 = <i>m<sup>2</sup> </i>

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Identifiers

10.1142/S1793042123500458

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5881035

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