V. Ziegler

most citedOn Pillai's Problem involving Lucas sequences of the second kind

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2026

Product of powers of distinct primes as sums of Fibonacci numbers

Herbert Batte, Florian Luca, Volker Ziegler

Let $F_{n}$ be the $n$ -th Fibonacci number. In this paper, we study the Diophantine equation $F_{n} + F_{m} = p^{x} q^{y}$ in nonnegative integers $n \geq m$ , $x$ and $y$ , where $p$ and $q$ are fix…

math.NT2026

Rational integers as sums of units -- the quadratic case

Christopher Frei, Martin Widmer, Volker Ziegler

How many natural numbers below $X$ can be written as a sum of $k$ units of the ring of integers of a given number field? We give the asymptotics as $X$ gets large for quadratic num…

math.NT2023★ 1 cited

On Pillai's Problem involving Lucas sequences of the second kind

Sebastian Heintze, Volker Ziegler

In this paper we consider the Diophantine equation $V_{n} - b^{m} = c$ for given integers $b, c$ with $b \geq 2$ , whereas $V_{n}$ varies among Lucas-Lehmer sequences of the second…

math.NT2023

On a conjecture of Levesque and Waldschmidt

Tobias Hilgart, Volker Ziegler

One of the first parametrised Thue equations, $X^{3} - (n - 1) X^{2} Y - (n + 2) X Y^{2} - Y^{3} = 1,$ over the integers was solved by E. Thomas in 1990. If we interpret this as…

math.NT2023

On sums of two Fibonacci numbers that are powers of numbers with limited Hamming weight

Ingrid Vukusic, Volker Ziegler

In 2018, Luca and Patel conjectured that the largest perfect power representable as the sum of two Fibonacci numbers is $386 4^{2} = F_{36} + F_{12}$ . In other words, they conjectured…