Another generalization of the Fibonacci and Lucas numbers

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 16, 2010, Number 3, Pages 11—17
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Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales,
PO Box 123, Kensington, NSW 1465, Australia


This paper considers some generalizations of the Fibonacci and Lucas numbers which are essentially ratios of the former, and hence not necessarily integers. Nevertheless, some new and elegant results emerge as well as variations on well-established identities.


  • Fibonacci numbers
  • Fundamental Lucas numbers
  • Primordial Lucas Numbers
  • Simson’s identity

AMS Classification

  • 11B39
  • 97F60


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Cite this paper

Shannon, A. G. (2010). Another generalization of the Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 16(3), 11-17.

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