D(z)-quadruples in Z[√-2]
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 1.8 (Dujella, 2026). Characterize elements $z$ of the ring $\mathbb{Z}[\sqrt{-2}]$ for which there exists a $D(z)$-quadruple.
Remark. Partial results on (non)existence of $D(z)$-quadruples in $\mathbb{Z}[\sqrt{-2}]$ were obtained by Abu Muriefah and Al-Rashed (Math. Commun. 9 (2004), 1–8), Franušić (Math. Commun. 9 (2004), 141–148), Dujella and Soldo (An. Ştiinţ. Univ. ``Ovidius'' Constanţa Ser. Mat. 18 (2010), 81–98), et Soldo (Miskolc Math. Notes 14 (2013), 265–277).
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 1.8
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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