Quadruples sharing their largest element
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 4.3 (Dujella, 2026). Are there infinitely many pairs of Diophantine quadruples with the same largest element?
Remark. Gibbs (1999) found three such pairs: $\{1,16640,16899,1124864520\}$ and $\{1,399,703920,1124864520\}$, $\{120,145673,154155,10778986831096\}$ and $\{8,120,2805566778,10778986831096\}$, $\{528,3253511,3336933,22929452257545400\}$ and $\{15,528,723737525421,22929452257545400\}$. Dujella (2026) found the fourth example: $\{528,1470,2274769665919896,7062345445140145061720\}$ and $\{528,1829619951,1827654733,7062345445140145061720\}$.
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 4.3
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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