Nonextendibility of \(D(-1)\)-triples of the form \(\{1,10,c\}\)

DOI10.1155/IJMMS.2005.2217zbMath1085.11016MaRDI QIDQ2576019

Alan Filipin

Publication date: 7 December 2005

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/52253

zbMATH Keywords

Pell equationsDiophantine \(m\)-tuple\(D(-1)\)-quadruples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45) Approximation to algebraic numbers (11J68)

Related Items (7)

\(D(-1)\)-triples of the form \(\{1,b,c\}\) in the ring \(\mathbb Z[\sqrt{-t}\), \(t>0\)] ⋮ On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension ⋮ On \(D(-1)\)-quadruples ⋮ Extensions of the \(D(\mp k^2)\)-triples \(\{k^2,k^2 \pm 1, 4k^2 \pm 1\}\) ⋮ On the family of Diophantine triples \(\{k+1,4k,9k+3\}\) ⋮ On a family of Diophantine triples \(\{k,A^2k+2A,(A+1)^2k+2(A+1)\}\) with two parameters ⋮ 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

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