Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 55-70.

TRIANGULAR DIOPHANTINE TUPLES FROM {1, 2}

Alan Filipin and László Szalay

Institute of Informatics and Mathematics, University of Sopron, Bajcsy Zs. u. 4., Sopron 9400, Hungary
Department of Mathematics, J. Selye University, Hradná str. 21, Komárno 945 01, Slovakia
e-mail: szalay.laszlo@uni-sopron.hu

Abstract.   In this paper, we prove that there does not exist a set of four positive integers {1, 2, c, d} such that a product of any two of them increased by 1 is a triangular number.

2020 Mathematics Subject Classification.   11D09, 11B37, 11J86.

Key words and phrases.   Diophantine m-tuples, Pell equations, linear forms in logarithms.

DOI: https://doi.org/10.21857/ygjwrcp48y

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