Polynomial-exponential equations and linear recurrences
Clemens Fuchs · Glasnik Matematicki · 2003
Let K be an algebraic number field and let (Gn) be a linear recurring sequence defined bywhere λ 1 , α 1 , . . ., αt are non-zero elements of K and whereIn 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 [8]) to calculate an upper bound for the number of solutions (n, x) under some additional assumptions.