There does not exist a \(D(4)\)-sextuple

DOI10.1016/j.jnt.2007.07.012zbMath1144.11029OpenAlexW2068578745MaRDI QIDQ927706

Alan Filipin

Publication date: 9 June 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.07.012

zbMATH Keywords

Diophantine \(m\)-tuples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Diophantine equations in many variables (11D72)

Related Items (10)

Extension of a Diophantine triple with the property \(D(4)\) ⋮ The extension of the \(D(-k^2)\)-pair \(\left\{k^2, k^2+1\right\}\) ⋮ On the \(D(4)\)-pairs \(\{a, ka\}\) with \(k\in \{2,3,6\}\) ⋮ \(D(4)\)-triples with two largest elements in common ⋮ There are only finitely many \(D(4)\)-quintuples ⋮ Two-parameter families of uniquely extendable Diophantine triples ⋮ Extensions of the \(D(\mp k^2)\)-triples \(\{k^2,k^2 \pm 1, 4k^2 \pm 1\}\) ⋮ Nonexistence of \(D(4)\)-quintuples ⋮ 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

Cites Work

• On the size of sets in which \(xy + 4\) is always a square
• Fibonacci numbers and sets with the property \(D(4)\)
• Logarithmic forms and group varieties.
• On Diophantine quintuples
• Solving constrained Pell equations
• There are only finitely many Diophantine quintuples
• Some rational Diophantine sextuples
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• On the number of solutions of simultaneous Pell equations
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