Two nested quadruples
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 4.4 (Dujella, 2026). Do there exist two Diophantine quadruples $\{a_1,b,c,d\}$ and $\{a_2,b,c,d\}$ such that $a_1<a_2<b<c<d$?
Remark. It was shown by Cipu, Dujella and Fujita (Mediterr. J. Math. 19 (2022), Article 187) that there are only finitely many such examples; in fact, the largest element satisfies $d < 10^{10^{26}}$.
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 4.4
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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