Diophantine Problems with Linear Recurrences via the Subspace Theorem
نویسنده
چکیده
In this paper we give an overview over recent developments (initiated by P. Corvaja and U. Zannier in [3]) on Diophantine problems where linear recurring sequences are involved and which were solved by using W.M. Schmidt’s Subspace Theorem. Moreover, as a new application, we show: let (Gn) and (Hn) be linear recurring sequences of integers defined by Gn = c1α n 1 + c2α n 2 + · · ·+ ctα t and Hn = d1β 1 + d2β 2 + · · ·+ dsβ s , where t, s ≥ 2, ci, dj are non-zero rational numbers and where α1 > . . . αt > 0, β1 > . . . > βs > 0 are integers with α1, α2 · · ·αtβ1 · · ·βs coprime, and let > 0. Then, we have G.C.D.(Gn, Hn) < exp( n) for all n large enough.
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