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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

Open Access
|Mar 2015

References

  1. [1] BENJAMIN, A.-QUINN, J.: The Fibonacci numbers - Exposed more discretely, Math. Mag. 76 (2003), 182-192.
  2. [2] HALTON, J. H.: On the divisibility properties of Fibonacci numbers, Fibonacci Quart. 4 (1966), 217-240.
  3. [3] KALMAN, D.-MENA, R.: The Fibonacci numbers - exposed, Math. Mag. 76 (2003), 167-181.
  4. [4] KOSHY, T.: Fibonacci and Lucas Numbers with Applications. Wiley, New York, 2001.10.1002/9781118033067
  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.10.1155/2011/407643
  6. [6] MARQUES, D.: On the order of appearance of integers at most one away from Fibonacci numbers, Fibonacci Quart. 50 (2012), 36-43.
  7. [7] MARQUES, D.: The order of appearance of product of consecutive Fibonacci numbers, Fibonacci Quart. 50 (2012), 132-139.
  8. [8] MARQUES, D.: The order of appearance of powers Fibonacci and Lucas numbers, Fibonacci Quart. 50 (2012), 239-245.
  9. [9] MARQUES, D.: The order of appearance of product of consecutive Lucas numbers, Fibonacci Quart. 50 (2012), 239-245.
  10. [10] MARQUES, D.: Sharper upper bounds for the order of appearance in the Fibonacci sequence, Fibonacci Quart. 51 (2013), 233-238.
  11. [11] LAGARIAS, J. C.: The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math. 118 (1985), 449-461.10.2140/pjm.1985.118.449
  12. [12] LENGYEL, T.: The order of the Fibonacci and Lucas numbers, Fibonacci Quart. 33 (1995), 234-239.
  13. [13] RIBENBOIM, P.: My Numbers, My Friends: Popular Lectures on Number Theory. Springer-Verlag, New York, 2000.
  14. [14] ROBINSON, D.W.: The Fibonacci matrix modulo m, Fibonacci Quart. 1 (1963), 29-36.
  15. [15] SALLÉ, H. J. A.: Maximum value for the rank of apparition of integers in recursive sequences, Fibonacci Quart. 13 (1975), 159-161.
  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.
  17. [17] VOROBIEV, N. N.: Fibonacci Numbers. Birkhäuser, Basel, 2003. 10.1007/978-3-0348-8107-4
DOI: https://doi.org/10.2478/tmmp-2014-0019 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
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: 3 issues per year

© 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.