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Glasnik matematički, Vol. 38 No. 2, 2003.

Original scientific paper

Polynomial-exponential equations and linear recurrences

Clemens Fuchs

Full text: english pdf 657 Kb

page 233-252

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Abstract

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

Gn = + P2(n) + ... + Pt(n) ,

where , , ... , 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.

Keywords

Polynomial-exponential equations; linear recurrences; Subspace-Theorem

Hrčak ID:

1317

URI

https://hrcak.srce.hr/1317

Publication date:

1.12.2003.

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