Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Arithmetical study of a certain ternary recurrence sequence and related questions


Authors: M. Mignotte and N. Tzanakis
Journal: Math. Comp. 61 (1993), 901-913
MSC: Primary 11B37
DOI: https://doi.org/10.1090/S0025-5718-1993-1185248-8
MathSciNet review: 1185248
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The complete solution in $ (n,{y_1},{y_2}) \in {{\mathbf{Z}}^3}$ of the Diophantine equation

$\displaystyle {b_n} = \pm {2^{{y_1}}}{3^{{y_2}}}$

is given, where $ {({b_n})_{n \in {\mathbf{Z}}}}$ is Berstel's recurrence sequence defined by

$\displaystyle {b_0} = {b_1} = 0,\quad {b_2} = 1,\quad {b_{n + 3}} = 2{b_{n + 2}} - 4{b_{n + 1}} + 4{b_n}.$


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

  • [1] F. Beukers, The zero-multiplicity of ternary recurrences, Compositio Math. 77 (1991), 165-177. MR 1091896 (92a:11014)
  • [2] J. Blass, A. M. W. Glass, D. Manski, D. Meronk, and R. Steiner, Constants for lower bounds for linear forms in the logarithms of algebraic numbers. I: The general case, Acta Arith. 55 (1990), 1-14. MR 1056110 (91h:11063)
  • [3] J. H. Evertse, On sums of S-units and linear recurrences, Compositio Math. 53 (1984), 225-244. MR 766298 (86c:11045)
  • [4] M. Mignotte, A note on linear recursive sequences, J. Austral. Math. Soc. Ser. A 20 (1975), 242-244. MR 0384708 (52:5581)
  • [5] -, Détermination des répétitions d'une certaine suite récurrente linéaire, Publ. Math. Debrecen 33 (1986), 297-306. MR 883759 (88h:11012)
  • [6] M. Mignotte and N. Tzanakis, Arithmetical study of recurrence sequences, Acta Arith. 57 (1991), 357-364. MR 1109992 (92c:11013)
  • [7] M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257-283. MR 598881 (82h:10049)
  • [8] B. M. M. de Weger, Products of prime powers in binary recurrence sequences. II, Math. Comp. 47 (1986), 729-739. MR 856716 (87m:11027b)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11B37

Retrieve articles in all journals with MSC: 11B37


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1185248-8
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society