Bipartite Diophantine tuples and their applications
Number Theory
2026-03-17 v3
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.
Cite
@article{arxiv.2512.03441,
title = {Bipartite Diophantine tuples and their applications},
author = {Kin Ming Tsang and Chi Hoi Yip},
journal= {arXiv preprint arXiv:2512.03441},
year = {2026}
}
Comments
21 pages, revised based on referee comments