Regularity of D(4)-quadruples
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 4.7 (Dujella, 2026). Are all $D(4)$-quadruples regular?
Remark. A positive answer to Problem 4.7 would imply a positive answer to Problem 4.6, while a negative answer to Problem 4.6 would imply a negative answer to Problem 4.7. Namely, $\{a,b,c,d\}$ is a regular Diophantine quadruple if and only if $\{2a,2b,2c,2d\}$ is a regular $D(4)$-quadruple.
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 4.7
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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