A note on the extension of some triangular Diophantine sets

Alan Filipin; Ana Jurasić; Alain Togbé

doi:10.2478/auom-2026-0018

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A note on the extension of some triangular Diophantine sets

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 34 (2026): Issue 2 (July 2026)

By: Alan Filipin, Ana Jurasić and Alain Togbé

Open Access

|Jul 2026

Abstract

Let n be an integer. We call a set of m distinct positive integers a triangular D(n)-m-tuple if the product of its two distinct elements increased by n is the triangular number. In this paper, we consider the extension of the triangular D(k)-pair {k, 2k}, for k = 10 and k = 28, and prove that such a set cannot be extended to a quadruple.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2026-0018 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 29 - 43

Submitted on: Jul 4, 2025

Accepted on: Jan 8, 2026

Published on: Jul 11, 2026

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Keywords:

Diophantine sets,

system of Pell-like equations,

linear forms in logarithms

Related subjects:

Mathematics,

General mathematics

© 2026 Alan Filipin, Ana Jurasić, Alain Togbé, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 34 (2026): Issue 2 (July 2026)