Diophantine quadruple congruent mod k
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 4.5 (Dujella, 2026). Is there any Diophantine quadruple $\{a,b,c,d\}$ such that $a \equiv b \equiv c \equiv d \pmod{k}$ with $k \geqslant 3$?
Remark. It was shown by Dujella and Saradha (Indag. Math. (N.S.) 25 (2014), 131–136) that a positive answer to Problem 4.6 would imply a negative answer to Problem 4.5.
Preview rendered with KaTeX — the compiled PDF is the reference layout.
Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 4.5
Reproduit à des fins pédagogiques non commerciales, avec attribution à l'auteur. Problème de recherche ouvert : aucune solution connue à ce jour.
Downloads
PDFs are produced by the GitHub Actions pipeline: they may be missing in local development.
＋ Add to problem set