Original scientific paper

The extensibility of $D(4)$-pairs

Ljubica Baćić orcid.org/0000-0002-8634-4853 ; Nikola Andrić Primary School, Vukovar, Croatia
Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, zagreb, Croatia

Abstract

The set of $m$ positive integers with the property that the product of any two of them increased by $4$ is a perfect square is called a $D(4)$-$m$-tuple. In this paper we consider the extensibility of general $D(4)$-pair $\{a,b\}$ and prove some results that support the conjecture that there does not exist a $D(4)$-quintuple.

Keywords

Diphantine tuples; system of Diophantine equations

Hrčak ID:

110851

URI

https://hrcak.srce.hr/110851

Publication date:

19.11.2013.

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