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Diophantine triples with three parameters

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Abstract

According to well-known conjectures, for \(n=1\) or 4, any D(n)-triple has unique prolongation to D(n)-quadruple obtained by adjoining a larger element. For the first time, these conjectures are examined in case the triples depend on three integer parameters. Unicity of extension is established under various additional hypotheses on parameters.

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Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit nr. 7, R0-014700, P.O. Box 1-764, Bucharest, Romania

    Mihai Cipu

  2. Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1, Shin-ei, Narashino, Chiba, Japan

    Yasutsugu Fujita

  3. Département de Mathématique, Université de Strasbourg, 67084, Strasbourg, France

    Maurice Mignotte

Authors
  1. Mihai Cipu
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  2. Yasutsugu Fujita
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  3. Maurice Mignotte
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Correspondence to Yasutsugu Fujita.

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Cipu, M., Fujita, Y. & Mignotte, M. Diophantine triples with three parameters. Res. number theory 10, 44 (2024). https://doi.org/10.1007/s40993-024-00530-9

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