Integers represented by Lucas sequences
L. Hajdu, R. Tijdeman

TL;DR
This paper investigates the sets of integers that appear as the n-th terms of Lucas sequences, establishing bounds on their size and growth, with results that are sharp for large n and independent of sequence parameters.
Contribution
It introduces bounds on the size and growth of Lucas sequence terms that are independent of sequence parameters, a novel aspect in the study of these sequences.
Findings
Bounds on the size of sets of n-th Lucas sequence terms
Sharp bounds for large n
Growth order bounds independent of sequence parameters
Abstract
In this paper we study the sets of integers which are -th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for 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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