Bipartite Diophantine tuples and their applications (2512.03441v1)

Published 3 Dec 2025 in math.NT

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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