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arXiv · 2512.03441

Bipartite Diophantine tuples and their applications

Kin Ming Tsang·Chi Hoi Yip
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Abstract

This paper investigates bipartite variants of generalized Diophantine tuples and their applications. We generalize a result of Bugeaud--Dujella on a special family of bipartite Diophantine tuples and affirmatively resolve a related question posed by the second author. Additionally, we establish new connections between bipartite Diophantine tuples and several known variants of Diophantine tuples, including those introduced by Banks--Luca--Szalay and Kihel--Kihel.

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Kin Ming Tsang, Chi Hoi Yip. 2025-12-03. Bipartite Diophantine tuples and their applications. https://doi.org/10.1007/s40993-026-00709-2

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