Products close to a perfect power
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 1.6 (Dujella, 2026). Prove unconditionally that the size of a set of positive integers with the property that the product of any two of its distinct elements is 1 less than a perfect power is bounded by an absolute constant.
Remark. Luca (Glas. Mat. Ser. III 40 (2005), 13–20) proved this result under the assumption that the abc-conjecture is valid.
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Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 1.6
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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