Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Equations $ au\sp l\sb n=bu\sp k\sb m$ satisfied by members of recurrence sequences


Authors: H. P. Schlickewei and W. M. Schmidt
Journal: Proc. Amer. Math. Soc. 118 (1993), 1043-1051
MSC: Primary 11B37
DOI: https://doi.org/10.1090/S0002-9939-1993-1152290-4
MathSciNet review: 1152290
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\{ {u_n}\} _{n \in \mathbb{Z}}}$ be a linear recurrence sequence. Given $ a \ne 0,\,b \ne 0$, and natural $ k \ne l$, we study equations as indicated in the title in unknowns $ n,m$. It turns out that under natural conditions on the sequence $ \{ {u_n}\} $, there are only finitely many solutions.


References [Enhancements On Off] (What's this?)

  • [1] J.-H. Evertse, On sums of $ S$-units and linear recurrences, Compositio Math. 53 (1984), 225-244. MR 766298 (86c:11045)
  • [2] M. Laurent, Equations exponentielles-polynômes et suites récurrentes. II, J. NumberTheory 31 (1989), 24-53. MR 978098 (90b:11023)
  • [3] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. I, Dritte Auflage, Springer, Berlin, Göttingen, Heidelberg, and New York, 1964.
  • [4] A. J. van der Poorten and H. P. Schlickewei, Zeros of recurrence sequences, Bull. Austral. Math. Soc. 44 (1991), 215-223. MR 1126359 (93d:11017)
  • [5] H. P. Schlickewei, Multiplicities of algebraic linear recurrences, Acta Math. (to appear). MR 1226526 (94i:11015)
  • [6] H. P. Schlickewei and W. M. Schmidt, On polynomial-exponential equations (to appear). MR 1219906 (94e:11032)
  • [7] -, Linear equations in members of recurrence sequences (to appear).
  • [8] -, The intersection of recurrence sequences (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11B37

Retrieve articles in all journals with MSC: 11B37


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152290-4
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society