On Arithmetic Progressions in Lucas Sequences
Lajos Hajdu
Institute of Mathematics
University of Debrecen
P. O. Box 400
H-4002 Debrecen
Hungary
Márton Szikszai
Institute of Mathematics, University of Debrecen
and
MTA-DE Research Group Equations Functions and Curves
Hungarian Academy of Sciences and University of Debrecen
P. O. Box 400
H-4002 Debrecen
Hungary
Volker Ziegler
Institute of Mathematics
University of Salzburg
Hellbrunnerstrasse 34/I
A-5020 Salzburg
Austria
Abstract:
In this paper, we consider arithmetic progressions contained in Lucas
sequences of the first and second kind. We prove that for almost all
Lucas sequences, there are only finitely many arithmetic three term
progressions and their number can be effectively bounded. We also show
that there are only a few Lucas sequences which contain infinitely many
arithmetic three term progressions and one can explicitly list both the
sequences and the progressions in them. A more precise statement is
given for sequences with dominant zero.
Full version: pdf,
dvi,
ps,
latex
(Concerned with sequences
A000032
A000045
A001045
A014551
A039834.)
Received March 20 2017; revised versions received August 7 2017; August 11 2017.
Published in Journal of Integer Sequences, September 3 2017.
Return to
Journal of Integer Sequences home page