8 papers
Four-square polynomial triples: quadratic classification and equal-degree obstructions
Mirela Jukić Bokun, Ana Jurasić
We study triples of distinct nonconstant polynomials over , or for which are all polyn…
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 Bujačić Babić, Ana Jurasić
We prove that every Diophantine quadruple over that contains at least one non-constant polynomial is regular; that is, $$(a+b-c-d)^2=4(ab+1)(cd+1).…
On exotic Diophantine triples in
Ana Jurasić
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 Jurasić
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 Jurasić
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…
A polynomial variant of a problem of Diophantus and its consequences
Alan Filipin, Ana Jurasić
We prove that every Diophantine quadruple in is regular. More precisely, we prove that if is a set of four non-zero polynomials from $\mathbb{R}[X]…
Elementary resolution of a family of quartic Thue equations over function fields
Clemens Fuchs, Ana Jurasić, Roland Paulin
We consider and completely solve the parametrized family of Thue equations \begin{eqnarray*}X(X-Y)(X+Y)(X-λY)+Y^4=ξ,\end{eqnarray*} where the solutions come from the ring $\m…