Sextuple pairs with square denominators
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 3.12 (Dujella, 2026). Are there infinitely many pairs of rational Diophantine sextuples sharing a common triple such that denominators of all elements (in the lowest terms) in the sextuples are perfect squares?
Remark. In 2024, Rathbun found two pairs of such sextuples. One such pair is \[ \{3/2^2, -12/5^2, -127500/389^2, -2093/50^2, 72512/265^2, -271859133/27970^2\}, \] \[ \{3/2^2, -12/5^2, -127500/389^2, 2387/50^2, 435252/685^2, -38178413/6130^2\}. \]
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 3.12
Reproduit à des fins pédagogiques non commerciales, avec attribution à l'auteur. Problème de recherche ouvert : aucune solution connue à ce jour.
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