4 papers
On a conjecture of Levesque and Waldschmidt II
Tobias Hilgart, Volker Ziegler
Related to Shank's notion of simplest cubic fields, the family of parametrised Diophantine equations, \[ x^3 - (n-1) x^2 y - (n+2) xy^2 - 1 = \left( x - λ_0 y\right) \left(x-λ_1 y\…
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 . In other words, they conjectured…
Twisted Thue equations with multiple exponents in fixed number fields
Tobias Hilgart, Volker Ziegler
Let be a number field of degree and fix multiplicatively independent algebraic integers that fulfil some technical requirements, which c…
On corner avoidance of -adic Halton sequences
Markus Hofer, Volker Ziegler
We consider the corner avoiding property of -dimensional -adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that t…