Ana Jurasic

collaborators

5 papers

math.NT2026

Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple

Ana Jurasić, Matej Jurasić

A set ${a, b, c}$ of distinct positive integers is called a Diophantine triple if $ab + 1$ , $a c + 1$ , and $b c + 1$ are perfect squares. Dujella formulated the conjecture that the only in…

math.NT2026

Regularity of Diophantine quadruples over $Q (i) [X]$

Sanda Bujačić Babić, Ana Jurasić

We prove that every Diophantine quadruple ${a, b, c, d}$ over $Q (i) [X]$ that contains at least one non-constant polynomial is regular; that is, $$(a+b-c-d)^2=4(ab+1)(cd+1).…

math.NT2026

On exotic Diophantine triples in $R [X]$

Ana Jurasić

Originally, an exotic Diophantine triple is a set ${a, b, c}$ of distinct nonzero rational numbers for which \[ a+1,\quad b+1,\quad c+1,\quad ab+1,\quad ac+1,\quad bc+1,\quad abc+1…

math.NT2026

Four squares from three real polynomials

Ana Jurasić

We construct three nonconstant polynomials $a, b, c \in R [X]$ such that \[ab+1,\qquad ac+1,\qquad bc+1,\qquad abc+1 \] are all squares in $R [X]$ . The entries in the…

math.NT2026

The extensibility of the Diophantine triple ${2, b, c}$

Nikola Adžaga, Alan Filipin, Ana Jurasić

The aim of this paper is to consider the extensibility of the Diophantine triple ${2, b, c}$ , where $2 < b < c$ , and to prove that such a set cannot be extended to an irregular Diophan…

Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple

Regularity of Diophantine quadruples over Q(i)[X]

On exotic Diophantine triples in R[X]

Four squares from three real polynomials

The extensibility of the Diophantine triple {2,b,c}

Regularity of Diophantine quadruples over $Q (i) [X]$

On exotic Diophantine triples in $R [X]$

The extensibility of the Diophantine triple ${2, b, c}$