On the family of Diophantine triples \(\{k+1,4k,9k+3\}\)

DOI10.1007/s10998-009-9059-6zbMath1199.11075OpenAlexW2023146651MaRDI QIDQ1046810

Bo He, Alain S. Togbé

Publication date: 29 December 2009

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

Full work available at URL: https://doi.org/10.1007/s10998-009-9059-6

zbMATH Keywords

Diophantine approximationlinear forms in logarithmsPell 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) Linear forms in logarithms; Baker's method (11J86) Approximation to algebraic numbers (11J68)

Related Items

On \(D(-1)\)-triples \(\{1,4p^2+1,1-p\}\) in the ring \(\mathbb{Z}[\sqrt{-p}\) with a prime \(p\)] ⋮ The regularity of Diophantine quadruples ⋮ There is no Diophantine quintuple ⋮ Elliptic curve involving subfamilies of rank at least 5 over $\mathbb{Q}(t)$ or $\mathbb{Q}(t,k)$ ⋮ Extensions of the \(D(\mp k^2)\)-triples \(\{k^2,k^2 \pm 1, 4k^2 \pm 1\}\) ⋮ Bounds on the number of Diophantine quintuples ⋮ The extendibility of Diophantine pairs. II: Examples

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