Volker Ziegler

collaborators

2 papers

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 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…

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

On a conjecture of Levesque and Waldschmidt II

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