Glasnik matematički, Vol. 38 No. 2, 2003.
Original scientific paper
Polynomial-exponential equations and linear recurrences
Clemens Fuchs
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
Publication date:
1.12.2003.
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