Z. Franusic

collaborators

3 papers

math.NT2026

Cardinalities of Jordan Diophantine sets of upper triangular integer matrices

Zrinka Franušić, Tomislav Pejković

Let $U$ be the ring of upper triangular $2 \times 2$ integer matrices. For $N \in U$ , a Jordan $D (N)$ -set is a set of distinct nonzero matrices in $U$ such that $(A B + B A) /2 + N$ is a squ…

math.NT2026

$D (N)$ -quadruples in upper-triangular $2 \times 2$ integer matrices

Andrej Dujella, Zrinka Franušić

We introduce analogues of Diophantine $D (N)$ - $m$ -tuples in the noncommutative ring $M_{2} (Z)$ of $2 \times 2$ integer matrices. Besides definitions based on the standard matrix…

math.NT2019

On the extensions of the Diophantine triples in Gaussian integers

Nikola Adžaga, Alan Filipin, Zrinka Franušić

A Diophantine $m$ -tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. In this paper we study the extensibility…

Cardinalities of Jordan Diophantine sets of upper triangular integer matrices

D(N)-quadruples in upper-triangular 2×2 integer matrices

On the extensions of the Diophantine triples in Gaussian integers

$D (N)$ -quadruples in upper-triangular $2 \times 2$ integer matrices