Strong rational Diophantine <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si9.svg"><mml:mrow><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-triples

Andrej Dujella, Matteo Paganin, Mohammad Sadek

Type: Article

Publication Date: 2020-04-02

Citations: 3

DOI: https://doi.org/10.1016/j.indag.2020.03.007

View Publication

Locations

Indagationes Mathematicae - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Strong Diophantine Triples	2008	Andrej Dujella Vinko Petričcević
+ PDF Chat	Strong Eulerian triples	2018	Andrej Dujella Ivica Gusić Vinko Petričević Petra Tadić
+ PDF Chat	Rational Diophantine sextuples with strong pair	2024	Andrej Dujella Matija Kazalicki Vinko Petričević
+	Rational Diophantine sextuples with strong pair	2025	Andrej Dujella Matija Kazalicki Vinko Petričević
+	Rational Diophantine sextuples with square denominators	2019	Andrej Dujella Matija Kazalicki Vinko Petričević
+	The Diophantine equation 2𝑥²+1=3ⁿ	2003	Ming-Guang Leu Guan-Wei Li
+	There is no Diophantine quintuple	2018	Bo He Alain Togbé Volker Ziegler
+	Square-Free Integer	2010	Algebra Arithmetic
+	Diophantine triples with largest two elements in common	2020	Mihai Cipu Andrej Dujella Yasutsugu Fujita
+ PDF Chat	A note on the Diophantine equation 𝑥^{2𝑝}-𝐷𝑦²=1	1989	Mao Hua Le
+	Generalized Diophantine 𝑚-tuples	2021	Anup B. Dixit Seoyoung C. Kim M. Ram Murty
+ PDF Chat	A polynomial variant of diophantine triples in linear recurrences	2022	Clemens Fuchs Sebastian Heintze
+	Rational Diophantine Quadruples	2014	M. A. Gopalan V. Geetha
+	Diophantine triples with three parameters	2024	Mihai Cipu Yasutsugu Fujita Maurice Mignotte
+	A polynomial variant of a problem of Diophantus and its consequences	2017	Alan Filipin Ana Jurasić
+	A polynomial variant of a problem of Diophantus and its consequences	2017	Alan Filipin Ana Jurasić
+	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]	2009	Zrinka Franušić
+	On simultaneous diophantine approximations to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>ζ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mi>ζ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>	2014	Simon Dauguet Wadim Zudilin
+	The extensibility of Diophantine pairs<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">{</mml:mo><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">}</mml:mo></mml:math>	2007	Yasutsugu Fujita
+	On the system of Diophantine equations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:…	2015	Takafumi Miyazaki Florian Luca

Works That Cite This (3)

Action	Title	Year	Authors
+ PDF Chat	Divisibility by 2 on quartic models of elliptic curves and rational Diophantine D(q)-quintuples	2022	Mohammad Sadek Tuğba Yesin
+	Introduction	2024	Andrej Dujella
+	Rational Diophantine sextuples with strong pair	2025	Andrej Dujella Matija Kazalicki Vinko Petričević

Works Cited by This (21)

Action	Title	Year	Authors
+	On quadratic twists of elliptic curves y2 = x(x − 1)(x − λ)	2014	Andrej Dujella Ivica Gusić Luka Lasić
+	Algorithms for Modular Elliptic Curves	1992	J. E. Cremona
+ PDF Chat	Strong Diophantine Triples	2008	Andrej Dujella Vinko Petričcević
+ PDF Chat	The square-free sieve and the rank of elliptic curves	1991	Fernando Gouvêa Barry Mazur
+ PDF Chat	Rank Frequencies for Quadratic Twists of Elliptic Curves	2001	Karl Rubin Alice Silverberg
+	Rang de certaines familles de courbes elliptiques d'invariant donné	1998	Jean-François Mestre
+	On a problem of Diophantus for rationals	2012	Andrej Dujella Clemens Fuchs
+	Diophantos of Alexandria: A Study in the History of Greek Algebra	1964	Thomas L. Heath
+ PDF Chat	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>	1969	A. Baker H. Davenport
+	What is a Diophantine $m$-tuple?	2016	Andrej Dujella