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Complete Resolution Of A Family Of Twisted Thue Equations
Tobias Hilgart, Carina Premstaller, Volker Ziegler
One of the first infinite families of Thue equations, for , was solved by Thomas in 1990. This family is asso…
On the unique solvability of the simultaneous Pell equations and
Tobias Hilgart, Volker Ziegler
We consider the simultaneous Pell equations where are positive integers. We describe a procedure which, for any fixed ,…
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…
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 a conjecture of Levesque and Waldschmidt
Tobias Hilgart, Volker Ziegler
One of the first parametrised Thue equations, over the integers was solved by E. Thomas in 1990. If we interpret this as…
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 families of cubic split Thue equations parametrised by linear recurrence sequences
Tobias Hilgart
Let be two linear-recurrent sequences that meet a dominant root condition and a few more technical re…
On a family of cubic Thue Equations involving Fibonacci and Lucas numbers
Tobias Hilgart, Ingrid Vukusic, Volker Ziegler
Let denote the -th Fibonacci number and the -th Lucas number. We completely solve the family of cubic Thue equations and show tha…