V. Ziegler

collaborators

2 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…