The Hoggatt-Bergum conjecture on \(D(-1)\)-triples \(\{F_{2k+1}\), \(F_{2k+3}\), \(F_{2k+5}\}\) and integer points on the attached elliptic curves
type: Item
instance of: scholarly article
title: The Hoggatt-Bergum conjecture on \(D(-1)\)-triples \(\{F_{2k+1}\), \(F_{2k+3}\), \(F_{2k+5}\}\) and integer points on the attached elliptic curves
zbMATH Open document ID: 1248.11025
DOI: 10.1216/RMJ-2009-39-6-1907
author: Yasutsugu Fujita
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-01-05T00:00:00Z
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 5652731
Wikidata QID: Q123328432
describes a project that uses: ecdata
MaRDI profile type: Publication
cites work: Q3208737
cites work: THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2
cites work: On the number of solutions of simultaneous Pell equations
cites work: ON THE FAMILY OF DIOPHANTINE TRIPLES {k− 1,k+ 1, 16k3− 4k}
cites work: Lucas and fibonacci numbers and some diophantine Equations
cites work: Q4341641
cites work: Q4347183
cites work: Q4220462
cites work: Q4429273
cites work: A proof of the Hoggatt-Bergum conjecture
cites work: A parametric family of elliptic curves
cites work: An absolute bound for the size of Diophantine \(m\)-tuples
cites work: Diophantine \(m\)-tuples and elliptic curves
cites work: On the size of Diophantine \(m\)-tuples
cites work: There are only finitely many Diophantine quintuples
cites work: Effective solution of the D(-1)-quadruple conjecture
cites work: COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER
cites work: Q4215652
cites work: Q4515266
cites work: Nonextendibility of \(D(-1)\)-triples of the form \(\{1,10,c\}\)
cites work: Q3436123
cites work: The extensibility of Diophantine pairs \(\{k - 1,k+1\}\)
cites work: Computing integral points on elliptic curves
cites work: Q4163581
cites work: Modular arithmetic on elements of small norm in quadratic fields
cites work: Q4023805
cites work: An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II
cites work: Modular curves and the Eisenstein ideal
cites work: Q5804241
cites work: Euler's concordant forms
cites work: The implicational fragment of $R$-mingle
description: scientific article; zbMATH DE number 5652731