Integers represented by Lucas sequences

Published 9 Aug 2024 in math.NT | (2408.04982v1)

Abstract: In this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth order of the terms of Lucas sequences that are independent of the parameters of the sequence, which is a new feature.

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