Work

Bipartite Diophantine tuples and their applications

Year: 2026

Type: article

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.

Source: Research in Number Theory

DOI: 10.1007/s40993-026-00709-2

Authors: Kin Ming Tsang, Chi Hoi Yip

Institutions: University of British Columbia, Georgia Institute of Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funder: Natural Sciences and Engineering Research Council of Canada