V. Ziegler

activity

20152021

most citedOn a family of cubic Thue Equations involving Fibonacci and Lucas numbers

2 citations · 4 across the 6 of their papers we have counts for

collaborators

14 papers

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

Sums of Fibonacci numbers that are perfect powers

Volker Ziegler

Let us denote by $F_{n}$ the $n$ -th Fibonacci number. In this paper we show that for a fixed integer $y$ there exists at most one integer exponent $a > 0$ such that the Diophantine equ…

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…

math.NT2020

Finding all $S$ -Diophantine quadruples for a fixed set of primes $S$

Volker Ziegler

Given a finite set of primes $S$ and a $m$ -tuple $(a_{1}, \dots, a_{m})$ of positive, distinct integers we call the $m$ -tuple $S$ -Diophantine, if for each $1 \leq i < j \leq m$ the quantit…

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

On sums of Fibonacci numbers with few binary digits

On a family of unit equations over simplest cubic fields

Sums of Fibonacci numbers that are perfect powers

Consecutive tuples of multiplicatively dependent integers

Finding all S-Diophantine quadruples for a fixed set of primes S

Finding all $S$ -Diophantine quadruples for a fixed set of primes $S$