Bipartite Diophantine tuples and their applications

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.