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Fibonacci numbers in generalized Pell sequences

  • Jhon J. Bravo EMAIL logo and Jose L. Herrera
Published/Copyright: September 27, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 5

Abstract

In this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for Fibonacci numbers in the Pell sequence.

Keywords: Generalized Pell number; Fibonacci number; linear form in logarithms; reduction method
MSC 2010: Primary 11B39; Secondary 11J86

This work was supported by Projects VRI ID 4689 (University of Cauca) and Colciencias 110371250560.

Acknowledgement

We thank the reviewer for his/her thorough review and highly appreciate the comments and suggestions, which significantly contributed to improving the quality of the publication. J. J. B. was supported in part by Projects VRI ID 4689 (University of Cauca) and Colciencias 110371250560. J. L. H thanks the University of Cauca for support during his Ph.D. studies.

  1. (Communicated by Milan Paštéka)

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Received: 2019-10-05
Accepted: 2020-02-20
Published Online: 2020-09-27
Published in Print: 2020-10-27

© 2020 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Monadic pseudo BE-algebras
  3. Quadruple construction of decomposable double MS-algebras
  4. Fibonacci numbers in generalized Pell sequences
  5. Solutions of a generalized markoff equation in Fibonacci numbers
  6. Root separation for polynomials with reducible derivative
  7. Quadratic refinements of Young type inequalities
  8. Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
  9. Integration with respect to deficient topological measures on locally compact spaces
  10. Differential subordinations and Pythagorean means
  11. Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
  12. Unbounded oscillation of fourth order functional differential equations
  13. Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
  14. Entropy as an integral operator: Erratum and modification
  15. Unital topology on a unital l-group
  16. On the topological complexity of Grassmann manifolds
  17. Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
  18. Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
  19. Two semigroup rings associated to a finite set of meromorphic functions
https://doi.org/10.1515/ms-2017-0413
Keywords for this article
Generalized Pell number; Fibonacci number; linear form in logarithms; reduction method

Articles in the same Issue

  1. Regular papers
  2. Monadic pseudo BE-algebras
  3. Quadruple construction of decomposable double MS-algebras
  4. Fibonacci numbers in generalized Pell sequences
  5. Solutions of a generalized markoff equation in Fibonacci numbers
  6. Root separation for polynomials with reducible derivative
  7. Quadratic refinements of Young type inequalities
  8. Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
  9. Integration with respect to deficient topological measures on locally compact spaces
  10. Differential subordinations and Pythagorean means
  11. Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
  12. Unbounded oscillation of fourth order functional differential equations
  13. Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
  14. Entropy as an integral operator: Erratum and modification
  15. Unital topology on a unital l-group
  16. On the topological complexity of Grassmann manifolds
  17. Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
  18. Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
  19. Two semigroup rings associated to a finite set of meromorphic functions
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