Integers represented by Lucas sequences

The Ramanujan Journal, vol. 66

Abstract

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.

Authors 2

1. Lajos Hajdu corresponding

   University of Debrecen

   Affiliation as printed

   GTIDEA Professor, Institute of Mathematics, University of Debrecen, P. O. Box 400, Debrecen, 4002, Hungary

   HUN-REN DE Equations, Functions, Curves and Their Applications Research Group, Debrecen, Hungary

2. Rob Tijdeman Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Postbus 9512, 2300 RA, Leiden, The Netherlands