A. Dujella

collaborators

4 papers

math.NT2026

Infinite families of Diophantine quadruples in $Z [- 2]$ in the remaining exceptional congruence classes

Andrej Dujella, Ivan Soldo

We continue the study of $D (z)$ -quadruples in the ring $Z [- 2]$ . Motivated by the earlier classification due to the authors and by the subsequent partial results for…

math.NT2026

Differences of squares of upper-triangular $2 \times 2$ integer matrices

Andrej Dujella, Zrinka FranuÅ¡iÄ

We consider the problem of characterizing upper-triangular matrices $M = (p 0 r q) \in M_{2} (Z)$ which can be represented in the form $A^{2} - B^{2}$ with u…

math.NT2026

Seven squares from three numbers

Andrej Dujella, Matija Kazalicki, Vinko PetriÄeviÄ

We study triples {a,b,c} of distinct nonzero rational numbers such that a+1,b+1,c+1,ab+1,ac+1,bc+1 and abc+1 are all perfect squares. We prove that there exist infinitely many such…

math.NT2024

Asymptotics of $D (q)$ -pairs and triples via $L$ -functions of Dirichlet charaters

Nikola AdÅ¾aga, Goran DraÅ¾iÄ, Andrej Dujella +1

Let $q$ be an integer. A $D (q)$ - $m$ -tuple is a set of $m$ distinct positive integers $a_{1}, a_{2}, ..., a_{m}$ such that $a_{i} a_{j} + q$ is a perfect square for all $1 \leq i < j \leq…

Infinite families of Diophantine quadruples in Z[−2​] in the remaining exceptional congruence classes

Differences of squares of upper-triangular 2×2 integer matrices

Seven squares from three numbers

Asymptotics of D(q)-pairs and triples via L-functions of Dirichlet charaters

Infinite families of Diophantine quadruples in $Z [- 2]$ in the remaining exceptional congruence classes

Differences of squares of upper-triangular $2 \times 2$ integer matrices

Asymptotics of $D (q)$ -pairs and triples via $L$ -functions of Dirichlet charaters