Tobias Hilgart

collaborators

4 papers

math.NT2026

Complete Resolution Of A Family Of Twisted Thue Equations

Tobias Hilgart, Carina Premstaller, Volker Ziegler

One of the first infinite families of Thue equations, $F_{n} (X) = X^{3} - (n - 1) X^{2} Y - (n + 2) X Y^{2} - Y^{3} = \pm 1$ for $n \in Z$ , was solved by Thomas in 1990. This family is asso…

math.NT2024

On the unique solvability of the simultaneous Pell equations $x^{2} - a y^{2} = 1$ and $z^{2} - b x^{2} = 1$

Tobias Hilgart, Volker Ziegler

We consider the simultaneous Pell equations $x^{2} - a y^{2} = 1, z^{2} - b x^{2} = 1,$ where $a > b \geq 2$ are positive integers. We describe a procedure which, for any fixed $b$ ,…

math.NT2024

On split families of Thue equations with linear recurrence sequences as factors

Tobias Hilgart

We consider a parametrised family of Thue equations, \[ (x-G_1(n)\, y) \cdots (x-G_d(n)\, y) - y^d = \pm 1, \] which was first considered by Thomas to have an explicit set of solut…

math.NT2024

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 - Î»_0 y\right) \left(x-Î»_1…

Complete Resolution Of A Family Of Twisted Thue Equations

On the unique solvability of the simultaneous Pell equations x2−ay2=1 and z2−bx2=1

On split families of Thue equations with linear recurrence sequences as factors

On a conjecture of Levesque and Waldschmidt II

On the unique solvability of the simultaneous Pell equations $x^{2} - a y^{2} = 1$ and $z^{2} - b x^{2} = 1$