Some Golden Ratio generalized Fibonacci and Lucas sequences

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 22, 2016, Number 1, Pages 33–41
Full paper (PDF, 206 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney, NSW 2006, Australia

A. G. Shannon
Emeritus Professor, University of Technology Sydney, NSW 2007, Australia
Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia

Abstract

Various characteristics of the ordinary Fibonacci and Lucas sequences, many known for centuries, are shown to be common to generalized sequences related to the Golden Ratio. Periodicity properties are also investigated.

Keywords

• Unit digits (right-end-digits)
• Modular rings
• Golden Ratio
• reduced Pythagorean triples
• Fibonacci and Lucas numbers
• Pythagorean triples

AMS Classification

• 11B39
• 11B50

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