Almost rational Diophantine septuples
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 3.3 (Dujella, 2026). Are there infinitely many almost rational Diophantine septuples, i.e. sets of seven rationals such that all products increased by 1 are squares, with one exception?
Remark. Gibbs (2016) and Dujella-Kazalicki-Petričević (2018) found several examples of almost rational Diophantine septuples. For example, in $\{243/560, 1147/5040, 1100/63, 7820/567, 95/112, 38269/6480, 196/45\}$, the only missing condition is that $38269/6480 \cdot 196/45+1$ is not a square.
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 3.3
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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