From the 1 of 5 linked papers with an AI index.
5 papers
Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple
Ana Jurasić, Matej Jurasić
A set of distinct positive integers is called a Diophantine triple if , , and are perfect squares. Dujella formulated the conjecture that the only in…
Regularity of Diophantine quadruples over
Sanda BujaÄiÄ BabiÄ, Ana JurasiÄ
The paper proves that any Diophantine quadruple of polynomials over the ring \(\mathbb{Q}(i)[X]\) containing at least one non‑constant polynomial satisfies the regularity relation…
On exotic Diophantine triples in
Ana JurasiÄ
Originally, an exotic Diophantine triple is a set 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…
Four squares from three real polynomials
Ana JurasiÄ
We construct three nonconstant polynomials such that \[ab+1,\qquad ac+1,\qquad bc+1,\qquad abc+1 \] are all squares in . The entries in the…
The extensibility of the Diophantine triple
Nikola Adžaga, Alan Filipin, Ana JurasiÄ
The aim of this paper is to consider the extensibility of the Diophantine triple , where , and to prove that such a set cannot be extended to an irregular Diophan…