A. Dujella

activity

19982026

most citedOn the size of Diophantine m-tuples

61 citations · 439 across the 46 of their papers we have counts for

collaborators

47 papers

math.NT2026

Prime-power Diophantine tuples

Andrej Dujella

A positive $D (n)$ - $m$ -tuple is a set $A = {a_{1}, \dots, a_{m}}$ of distinct positive integers such that $a_{i} a_{j} + n$ is a square for every $i \neq = j$ . In 2005, Dujella and Luca obtained a…

math.NT2026

Ranks and integer points on elliptic curves induced by Fibonacci triples

Andrej Dujella

Let $F_{n}$ and $L_{n}$ denote the Fibonacci and Lucas numbers, respectively, and consider \[ E_k:\qquad y^2=(F_{2k}x+1)(F_{2k+2}x+1)(F_{2k+4}x+1). \] These elliptic curves arise natur…

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.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 Franušić

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 Petričević

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…

Prime-power Diophantine tuples

Ranks and integer points on elliptic curves induced by Fibonacci triples

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

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

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

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