Glasnik Matematicki, Vol. 38, No.2 (2003), 233-252.
POLYNOMIAL-EXPONENTIAL EQUATIONS AND LINEAR
RECURRENCES
Clemens Fuchs
Institut fur Mathematik, Technische Universitat Graz,
Steyrergasse 30, 8010 Graz, Austria
e-mail: clemens.fuchs@tugraz.at
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.
Full text (PDF) (free access)
Glasnik Matematicki Home Page