A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 13105132
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
Abstract
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 wellestablished identities.
Keywords

Fibonacci numbers

Fundamental Lucas numbers

Primordial Lucas Numbers

Simson’s identity
AMS Classification
 11B39
 97F60
References
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 Jerbic, Stephen K. 1968. Fibonomial Coefficients. Master of Arts Thesis, San Jose State College, California.
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 Shannon, A.G. 1974. Advanced Problem H233. The Fibonacci Quarterly. 12: 108.
 Whitney, Raymond E. 1970. On a Class of Difference Equations. The Fibonacci Quarterly. 8: 470475.
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Cite this paper
APAShannon, A. G. (2010). Another generalization of the Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 16(3), 1117.
ChicagoShannon, AG. “Another Generalization of the Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 16, no. 3 (2010): 1117.
MLAShannon, AG. “Another Generalization of the Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 16.3 (2010): 1117. Print.