Sums of S-units in recurrence sequences☆

Add time:08/16/2019    Source:sciencedirect.com

In this paper we give various finiteness results concerning terms of recurrence sequences Un representable as a sum of S-units with a fixed number of terms. We prove that under certain (necessary) conditions, the number of indices n for which Un allows such a representation is finite, and can be bounded in terms of the parameters involved. In this generality, our result is ineffective, i.e. we cannot bound the size of the exceptional indices. We also give an effective result, under some stronger assumptions.

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