The extendibility of $D(4)$-pairs

Ljubica Baćić, Alan Filipin


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.


Diphantine tuples, system of Diophantine equations

Full Text:


ISSN: 1331-0623 (Print), 1848-8013 (Online)