The extendibility of Diophantine pairs with property $D(-1)$

DOI10.11568/kjm.2020.28.3.539zbMath1481.11022OpenAlexW3093146890MaRDI QIDQ5152002

Jinseo Park

Publication date: 18 February 2021

Full work available at URL: http://dspace.kci.go.kr/handle/kci/662276?show=full

zbMATH Keywords

Fibonacci numberPellian equationDiophantine \(m\)-tuple

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension
• 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
• The extensibility of Diophantine pairs \(\{k - 1,k+1\}\)
• Logarithmic forms and group varieties.
• Sets in Which xy + k is Always a Square
• Solving constrained Pell equations
• A parametric family of elliptic curves
• There is no Diophantine quintuple
• COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER
• Effective solution of the D(-1)-quadruple conjecture

This page was built for publication: The extendibility of Diophantine pairs with property $D(-1)$