Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T00:25:50.868Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Fibonacci Quotient Fp-ε/p

Published online by Cambridge University Press:  20 November 2018

H. C. Williams
H. C. Williams*
Affiliation:
Department of Computer Science, University of Manitoba Winnipeg, Manitoba, R3T 2N2 Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note a formula analogous to Eisenstein's well known formula is presented for Fp-ε/p, where Fn is the nth Fibonacci number (F0 = 0, F1 = 1), p an odd prime, and

This formula is:

Keywords

10A3510A10Fibonacci numbers
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 366 - 370
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Andrews, G. H., Some Formulae for the Fibonacci sequence with generalizations, Fib. Quart., 7 (1969), 113-130.Google Scholar
2. Brillhart, J., Tonascia, J., and Weinberger, P., On the Fermat quotient, Computers in Number Theory, Academic Press, London and New York, 1971, pp 213-222.Google Scholar
3. Dickson, L. E., History of the Theory of Numbers, Vol. 1, Chelsea, New York, 1952.Google Scholar
4. Lehmer, D. H., An extended theory of Lucas' functions, Annals of Math. (2) 31 (1930), 419-448.Google Scholar
5. Wall, D. D., Fibonacci series modulo m, Amer. Math. Monthly. 67 (1960), 525-532.Google Scholar