Glasnik Matematicki, Vol. 38, No.2 (2003), 233-252.


Clemens Fuchs

Institut fur Mathematik, Technische Universitat Graz, Steyrergasse 30, 8010 Graz, Austria

Abstract.   Let K be an algebraic number field and let (Gn) be a linear recurring sequence defined by

Gn = λ1 α1n + P2(n) α2n + ... + Pt(n) αtn,

where λ1, α1, ... , αt are non-zero elements of K and where Pi(x) K[x] for i = 2, ... , t. Furthermore let f(z,x) K[z,x] monic in x. In this paper we want to study the polynomial-exponential Diophantine equation f(Gn, x) = 0. We want to use a quantitative version of W. M. Schmidt's Subspace Theorem (due to J.-H. Evertse) to calculate an upper bound for the number of solutions (n,x) under some additional assumptions.

2000 Mathematics Subject Classification.   11D45, 11D61.

Key words and phrases.   Polynomial-exponential equations, linear recurrences, Subspace-Theorem.

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