Bipartite Diophantine tuples and their applications
arXiv:2512.03441 · doi:10.1007/s40993-026-00709-2
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.
21 pages, revised based on referee comments