Author

Z. Franusic

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Preprint Oct 2026

Cardinalities of Jordan Diophantine sets of upper triangular integer matrices

Let $U$ be the ring of upper triangular $2\times2$ integer matrices. For $N\in U$, a Jordan $D(N)$-set is a set of distinct nonzero matrices in $U$ such that $(AB+BA)/2+N$ is a square in $U$ for any two distinct elements $A$ and $B$. We determine all $N$ for which an infinite Jordan $D(N)$-set exists. If no infinite se...

Z. Franušić, T. Pejković · 0 citations

Preprint Aug 2026

$D(N)$-quadruples in upper-triangular $2\times2$ integer matrices

We introduce analogues of Diophantine $D(N)$-$m$-tuples in the noncommutative ring $M_2(\mathbb Z)$ of $2\times2$ integer matrices. Besides definitions based on the standard matrix product, we consider a symmetric version defined via the Jordan product $$A\circ B=\frac12(AB+BA).$$ Special attention is devoted to upper-...

A. Dujella, Z. Franušić · 0 citations