Original scientific paper

https://doi.org/10.21857/ygjwrcpgoy

The problem of the extension of D(4)-triple {1, b, c}

Kouèssi Norbert Adédji orcid.org/0000-0001-8257-5729 ; Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-, BéninCalavi
Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia
Alain Togbé orcid.org/0000-0002-5882-936X ; Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, 1401 S, U.S. 421, Westville IN 46391 USA

Abstract

In this paper, we study the extensibility of the D(4)-triple {1, b, c}, where 1 < b < c, by proving that such a set cannot be extended to an irregular D(4)-quadruple only for some values of c. For this study, we will use the classical methods based on the resolution of the binary recurrence sequences with new approaches in order to confirm a conjecture of uniqueness of such an extension.

Keywords

Diophantine m-tuples; system of Pellian equations; reduction method; linear form in logarithms

Hrčak ID:

283925

URI

https://hrcak.srce.hr/283925

Publication date:

27.9.2022.

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