On a family of Diophantine triples \(\{K,A^2K + 2A, (A + 1)^2 K + 2(A + 1)\}\) with two parameters. II

DOI10.1007/s10998-012-9001-zzbMath1265.11054OpenAlexW2016017237MaRDI QIDQ2428641

Bo He, Alain S. Togbé

Publication date: 26 April 2012

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

Full work available at URL: https://doi.org/10.1007/s10998-012-9001-z

zbMATH Keywords

Diophantine quadruplessimultaneous Diophantine equationsDiophantine tuples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Cubic and quartic Diophantine equations (11D25) Linear forms in logarithms; Baker's method (11J86)

Related Items (10)

The extensibility of the \(D(\pm k)\)-triple \(\{k\mp 1,k, 4k\mp 1\}\) ⋮ The number of irregular Diophantine quadruples for a fixed Diophantine pair or triple ⋮ The extension of the \(D(-k^2)\)-pair \(\left\{k^2, k^2+1\right\}\) ⋮ The regularity of Diophantine quadruples ⋮ There is no Diophantine quintuple ⋮ Two-parameter families of uniquely extendable Diophantine triples ⋮ Diophantine triples with largest two elements in common ⋮ Diophantine pairs that induce certain Diophantine triples ⋮ Bounds on the number of Diophantine quintuples ⋮ An infinite two-parameter family of Diophantine triples

Cites Work

• On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension
• Verification of a conjecture of E. Thomas
• On a family of Diophantine triples \(\{k,A^2k+2A,(A+1)^2k+2(A+1)\}\) with two parameters
• An absolute bound for the size of Diophantine \(m\)-tuples
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• There are only finitely many Diophantine quintuples

This page was built for publication: On a family of Diophantine triples \(\{K,A^2K + 2A, (A + 1)^2 K + 2(A + 1)\}\) with two parameters. II