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Diophantine equations in separated variables and polynomial power sums
Clemens Fuchs, Sebastian Heintze
We consider Diophantine equations of the shape , where the polynomials and are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we…
A function field variant of Pillai's problem
Clemens Fuchs, Sebastian Heintze
In this paper, we consider a variant of Pillai's problem over function fields in one variable over . For given simple linear recurrence sequences and $…
Integral zeros of a polynomial with linear recurrences as coefficients
Clemens Fuchs, Sebastian Heintze
Let be a number field, a finite set of places of , and be the ring of -integers. Moreover, let $$ G_n^{(0)} Z^d + \cdots + G_n^{(d-1)} Z + G…
A Polynomial Variant of Diophantine Triples in Linear Recurrences
Clemens Fuchs, Sebastian Heintze
Let be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation $ G_n = f_1α_1^n + \cdots + f_…
Norm form equations with solutions taking values in a multi-recurrence
Clemens Fuchs, Sebastian Heintze
We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many values in each c…
On the growth of linear recurrences in function fields
Clemens Fuchs, Sebastian Heintze
Let be a non-degenerate linear recurrence sequence with power sum representation . In this paper we will prov…