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Extensions of the triangular D(3)-Pair {3, 6}

  • Alan Filipin , Ana Jurasić EMAIL logo und László Szalay
Veröffentlicht/Copyright: 9. August 2025
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Abstract

In this paper, we prove that there does not exist a set of four positive integers {3, 6, c, d}, such that a product of any two of them increased by 3 is a triangular number.


The first and the second author were supported by Croatian Science Fund, grant number IP-2022-10-5008. The second author was supported by the University of Rijeka project uniri-iskusni-period-23-66. The third author was supported by the Hungarian National Foundation for Scientific Research Grant No. 130909 and 150284. The first and the third author are also supported by bilateral Hungarian-Croatian project “Graphs and Diophantine equations in modeling molecular structures”. The part of the problem was done during the first author’s visit to Komárno, financially supported by SAIA scholarship. The authors want to thank to Sz. Tengely for allowing them the implementation of his algorithm in Sage and to both referees for very useful suggestions.


  1. (Communicated by Marco Cantarini)

References

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Received: 2024-11-05
Accepted: 2025-04-18
Published Online: 2025-08-09
Published in Print: 2025-08-26

© 2025 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0057/html
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