I. Vukusic

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20202025

U_{n} - b^{m} = c

2 citations · 5 across the 12 of their papers we have counts for

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math.NT2021

On a cubic Family of Thue Equations involving Fibonacci Numbers and Powers of Two

Ingrid Vukusic

In this paper we completely solve the family of parametrised Thue equations \[ X(X-F_n Y)(X-2^n Y)-Y^3=\pm 1, \] where $F_{n}$ is the $n$ -th Fibonacci number. In particular, for any…

math.NT2021★ 2 cited

On a family of cubic Thue Equations involving Fibonacci and Lucas numbers

Tobias Hilgart, Ingrid Vukusic, Volker Ziegler

Let $F_{n}$ denote the $n$ -th Fibonacci number and $L_{n}$ the $n$ -th Lucas number. We completely solve the family of cubic Thue equations $(X - F_{n} Y) (X - L_{n} Y) X - Y^{3} = \pm 1$ and show tha…

math.NT2021★ 1 cited

On sums of Fibonacci numbers with few binary digits

Ingrid Vukusic, Volker Ziegler

In this paper we completely solve the Diophantine equation $F_{n} + F_{m} = 2^{a_{1}} + 2^{a_{2}} + 2^{a_{3}} + 2^{a_{4}} + 2^{a_{5}}$ , where $F_{k}$ denotes the $k$ -th Fibonacci number. In addition to comple…

math.NT2021

On a family of unit equations over simplest cubic fields

Ingrid Vukusic, Volker Ziegler

Let $a \in Z$ and $ρ$ be a root of $f_{a} (x) = x^{3} - a x^{2} - (a + 3) x - 1$ , then the number field $K_{a} = Q (ρ)$ is called a simplest cubic field. In this paper we consider the fam…

math.NT2021

Consecutive tuples of multiplicatively dependent integers

Ingrid Vukusic, Volker Ziegler

This paper is concerned with the existence of consecutive pairs and consecutive triples of multiplicatively dependent integers. A theorem by LeVeque on Pillai's equation implies th…