V. Ziegler

activity

20102026

most citedOn a variant of Pillai's problem

21 citations · 52 across the 30 of their papers we have counts for

collaborators

Showing 2016Show all

5 papers · 1 filter

math.NT2016

On a variant of Pillai's problem II

Kwok Chi Chim, István Pink, Volker Ziegler

In this paper, we show that there are only finitely many $c$ such that the equation $U_{n} - V_{m} = c$ has at least two distinct solutions $(n, m)$ , where ${U_{n}}_{n \geq 0}$ and $\{V_…

math.NT2016★ 2 cited

There is no Diophantine quintuple

Bo He, Alain Togbè, Volker Ziegler

A set of $m$ positive integers ${a_{1}, a_{2}, \dots, a_{m}}$ is called a Diophantine $m$ -tuple if $a_{i} a_{j} + 1$ is a perfect square for all $1 \leq i < j \leq m$ . In 2004 Dujella prove…

math.NT2016★ 1 cited

Effective Resolution of Diophantine equations of the form $u_{n} + u_{m} = w p_{1}^{z_{1}} \dots p_{s}^{z_{s}}$

István Pink, Volker Ziegler

Let $u_{n}$ be a fixed non-degenerate binary recurrence sequence with positive discriminant, $w$ a fixed non-zero integer and $p_{1}, p_{2}, \dots, p_{s}$ fixed, distinct prime numbers. In th…

math.NT2016★ 21 cited

On a variant of Pillai's problem

Kwok Chi Chim, István Pink, Volker Ziegler

In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.

math.NT2016

Non-Minimality of the Width- $w$ Non-adjacent Form in Conjunction with Trace One $τ$ -adic Digit Expansions and Koblitz Curves in Characteristic Two

Daniel Krenn, Volker Ziegler

This article deals with redundant digit expansions with an imaginary quadratic algebraic integer with trace $\pm 1$ as base and a minimal norm representatives digit set. For $w\geq…

On a variant of Pillai's problem II

There is no Diophantine quintuple

Effective Resolution of Diophantine equations of the form un​+um​=wp1z1​​⋯pszs​​

On a variant of Pillai's problem

Non-Minimality of the Width-w Non-adjacent Form in Conjunction with Trace One τ-adic Digit Expansions and Koblitz Curves in Characteristic Two

Effective Resolution of Diophantine equations of the form $u_{n} + u_{m} = w p_{1}^{z_{1}} \dots p_{s}^{z_{s}}$

Non-Minimality of the Width- $w$ Non-adjacent Form in Conjunction with Trace One $τ$ -adic Digit Expansions and Koblitz Curves in Characteristic Two