8th Croatian Mathematical Congress

New results on D(4)-m-TUPLES

4 Jul 2024, 09:20

30m

D1 (Faculty of Economics and Business, J. J. Strossmayer University of Osijek)

Poster NT: Number Theory Poster session

Speaker

Pavao Radić

Description

Let $n\ne 0$ be an integer. A set of $m$ distinct positive integers is called a $D(n)$-$m$-tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. We present known results and mention open problems and conjectures related to $D(4)$-$m$-tuples. Also, the latest results from $[1]$ are shown.
References:
$[1]$ Bliznac Trebješanin, Marija; Radić, Pavao,
On extensions of D(4)-triples by adjoining smaller elements, Publicationes mathematicae, (2025)