D. Kreso

activity

20132023

D (n)

-sets for several

n

12 citations · 23 across the 9 of their papers we have counts for

collaborators

9 papers

math.NT2023

On equal values of products and power sums of consecutive elements in an arithmetic progression

András Bazsó, Dijana Kreso, Florian Luca +2

In this paper we study the Diophantine equation \begin{align*} b^k + \left(a+b\right)^k + &\left(2a+b\right)^k + \ldots + \left(a\left(x-1\right) + b\right)^k = \\ &y\left(y+c\righ…

math.NT2017

Diophantine equations in separated variables and lacunary polynomials

Dijana Kreso

We study Diophantine equations of type $f (x) = g (y)$ , where $f$ and $g$ are lacunary polynomials. According to a well known finiteness criterion, for a number field $K$ and nonconsta…

math.NT2017★ 12 cited

Triples which are $D (n)$ -sets for several $n$ 's

Nikola Adžaga, Andrej Dujella, Dijana Kreso +1

For a nonzero integer $n$ , a set of distinct nonzero integers ${a_{1}, a_{2}, \dots, a_{m}}$ such that $a_{i} a_{j} + n$ is a perfect square for all $1 \leq i < j \leq m$ , is called a Diophantine $…

math.NT2017

Decomposable polynomials in second order linear recurrence sequences

Clemens Fuchs, Christina Karolus, Dijana Kreso

We study elements of second order linear recurrence sequences $(G_{n})_{n = 0}^{\infty}$ of polynomials in $C [x]$ which are decomposable, i.e. representable as $G_{n} = g \circ h$ …

math.NT2016

Diophantine equations and the monodromy groups

Dijana Kreso, Robert F. Tichy

We study Diophantine equations of type f(x)=g(y), where both f and g have at least two distinct critical points and equal critical values at at most two distinct critical points. S…

math.NT2015★ 6 cited

Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials

Dijana Kreso, Robert F. Tichy

Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficie…

math.AG2014★ 5 cited

On factorizations of maps between curves

Dijana Kreso, Michael E. Zieve

We examine the different ways of writing a cover of curves $ϕ : C \to D$ over a field $K$ as a composition $ϕ = ϕ_{n} \circ ϕ_{n - 1} \circ \dots \circ ϕ_{1}$ , where each $ϕ_{i}$ is a cover of…

math.NT2013

Non-extensibility of the pair ${1, 3}$ to a Diophantine quintuple in $Z [- d]$

Zrinka Franušić, Dijana Kreso

We show that the Diophantine pair ${1, 3}$ can not be extended to a Diophantine quintuple in $Z [- 2]$ . This result completes the work of the first autho…

math.NT2013

Diophantine equations with Euler polynomials

D. Kreso, Cs. Rakaczki

In this paper we determine possible decompositions of Euler polynomials $E_{k} (x)$ , i.e. possible ways of writing Euler polynomials as a functional composition of polynomials of lowe…