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<p>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.</p>

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Bipartite Diophantine tuples and their applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月18日

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  • Kin Ming Tsang,
  • Chi Hoi Yip

摘要

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.