Multiple extensions of a quadruple
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 1.2 (Dujella, 2026). Is there any positive integer $k \geqslant 2$ such that the Diophantine quadruple $\{k-1, k+1, 4k, 16k^3-4k\}$ has more than one extension to a rational Diophantine quintuple?
Remark. Stoll (Acta Arith. 190 (2019), 239–261) proved that the extension is unique for $k = 2, 3, 4, 5$.
Preview rendered with KaTeX — the compiled PDF is the reference layout.
Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 1.2
Reproduit à des fins pédagogiques non commerciales, avec attribution à l'auteur. Problème de recherche ouvert : aucune solution connue à ce jour.
Downloads
PDFs are produced by the GitHub Actions pipeline: they may be missing in local development.
＋ Add to problem set