Author

A. Dujella

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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. Franusic · 0 citations

Preprint Sep 2026

Prime-power Diophantine tuples

A positive $D(n)$-$m$-tuple is a set $A=\{a_1,\ldots,a_m\}$ of distinct positive integers such that $a_i a_j+n$ is a square for every $i\ne j$. In 2005, Dujella and Luca obtained an absolute bound for the cardinality of a $D(p)$- or $D(-p)$-tuple of positive integers, uniformly in the prime $p$. We extend the underlyin...

A. Dujella · 0 citations