On the Diophantine equation : Higher-order recurrences
Authors:
Clemens Fuchs, Attila Petho and Robert F. Tichy
Journal:
Trans. Amer. Math. Soc. 355 (2003), 4657-4681
MSC (2000):
Primary 11D45; Secondary 11D04, 11D61, 11B37
DOI:
https://doi.org/10.1090/S0002-9947-03-03325-7
Published electronically:
June 10, 2003
MathSciNet review:
1990766
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a field of characteristic
and let
be a linear recurring sequence of degree
in
defined by the initial terms
and by the difference equation

with
![$A_0,\ldots,A_{d-1}\in\mathbf{K}[x]$](/tran/2003-355-11/S0002-9947-03-03325-7/gif-abstract0/img8.gif)

![$\mathbf{K}[x]$](/tran/2003-355-11/S0002-9947-03-03325-7/gif-abstract0/img10.gif)




has only finitely many solutions


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Additional Information
Clemens Fuchs
Affiliation:
Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
Email:
clemens.fuchs@tugraz.at
Attila Petho
Affiliation:
Institute for Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, PO Box 12, Hungary
Email:
pethoe@math.klte.hu
Robert F. Tichy
Affiliation:
Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
Email:
tichy@tugraz.at
DOI:
https://doi.org/10.1090/S0002-9947-03-03325-7
Keywords:
Diophantine equations,
linear recurring sequences,
$S$-unit equations
Received by editor(s):
October 18, 2002
Received by editor(s) in revised form:
February 7, 2003
Published electronically:
June 10, 2003
Additional Notes:
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT
The second author was supported by the Hungarian National Foundation for Scientific Research, Grant Nos. 29330 and 38225
Dedicated:
Dedicated to Wolfgang M. Schmidt on the occasion of his 70th birthday.
Article copyright:
© Copyright 2003
American Mathematical Society