Skip to main content
Have a personal or library account? Click to login
The Order of Appearance of the Product of Five Consecutive Lucas Numbers Cover

The Order of Appearance of the Product of Five Consecutive Lucas Numbers

Tatra Mountains Mathematical Publications
Volume 59 (2014): Issue 1 (June 2014)
By:  and    
Open Access
|Mar 2015
References

References

  1. [1] BENJAMIN, A.-QUINN, J.: The Fibonacci numbers - Exposed more discretely, Math. Mag. 76 (2003), 182-192.
    Search in Google Scholar
  2. [2] HALTON, J. H.: On the divisibility properties of Fibonacci numbers, Fibonacci Quart. 4 (1966), 217-240.
    Search in Google Scholar
  3. [3] KALMAN, D.-MENA, R.: The Fibonacci numbers - exposed, Math. Mag. 76 (2003), 167-181.
    Search in Google Scholar
  4. [4] KOSHY, T.: Fibonacci and Lucas Numbers with Applications. Wiley, New York, 2001.
    Open DOISearch in Google Scholar
  5. [5] MARQUES, D.: On integer numbers with locally smallest order of appearance in the Fibonacci sequence, Internat. J. Math. Math. Sci., Article ID 407643 (2011), 4 pages.
    Open DOISearch in Google Scholar
  6. [6] MARQUES, D.: On the order of appearance of integers at most one away from Fibonacci numbers, Fibonacci Quart. 50 (2012), 36-43.
    Search in Google Scholar
  7. [7] MARQUES, D.: The order of appearance of product of consecutive Fibonacci numbers, Fibonacci Quart. 50 (2012), 132-139.
    Search in Google Scholar
  8. [8] MARQUES, D.: The order of appearance of powers Fibonacci and Lucas numbers, Fibonacci Quart. 50 (2012), 239-245.
    Search in Google Scholar
  9. [9] MARQUES, D.: The order of appearance of product of consecutive Lucas numbers, Fibonacci Quart. 50 (2012), 239-245.
    Search in Google Scholar
  10. [10] MARQUES, D.: Sharper upper bounds for the order of appearance in the Fibonacci sequence, Fibonacci Quart. 51 (2013), 233-238.
    Search in Google Scholar
  11. [11] LAGARIAS, J. C.: The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math. 118 (1985), 449-461.
    Open DOISearch in Google Scholar
  12. [12] LENGYEL, T.: The order of the Fibonacci and Lucas numbers, Fibonacci Quart. 33 (1995), 234-239.
    Search in Google Scholar
  13. [13] RIBENBOIM, P.: My Numbers, My Friends: Popular Lectures on Number Theory. Springer-Verlag, New York, 2000.
    Search in Google Scholar
  14. [14] ROBINSON, D.W.: The Fibonacci matrix modulo m, Fibonacci Quart. 1 (1963), 29-36.
    Search in Google Scholar
  15. [15] SALLÉ, H. J. A.: Maximum value for the rank of apparition of integers in recursive sequences, Fibonacci Quart. 13 (1975), 159-161.
    Search in Google Scholar
  16. [16] VINSON, J.: The relation of the period modulo m to the rank of apparition of m in the Fibonacci sequence, Fibonacci Quart. 1 (1963), 37-45.
    Search in Google Scholar
  17. [17] VOROBIEV, N. N.: Fibonacci Numbers. Birkhäuser, Basel, 2003.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/tmmp-2014-0019 | Journal eISSN: 1338-9750 (formerly 1210-3195) | Journal ISSN: 1210-3195
Journal RSS Feed
Language: English
Page range: 65 - 77
Submitted on: Sep 2, 2014
Published on: Mar 11, 2015
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Fibonacci numbers,
Lucas numbers,
order of appearance,
p-adic order
Related subjects:
Mathematics,
General mathematics

© 2015 Diego Marques, Pavel Trojovský, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 59 (2014): Issue 1 (June 2014)
Previous article
Next article