Fibonacci and Lucas primes

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 2, Pages 49–59
Full paper (PDF, 131 Kb)

Details

Authors and affiliations

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

A. G. Shannon
Faculty of Engineering & IT, University of Technology Sydney
NSW 2007, Australia

Abstract

The structures of Fibonacci numbers, F_n, formed when n equals a prime, p, are analysed using the modular ring Z₅, Pascal’s Triangle as well as various properties of the Fibonacci numbers to calculate “Pascal-Fibonacci” numbers to test primality by demonstrating the many structural differences between the cases when F_n is prime or composite.

Keywords

• Fibonacci sequence
• Golden Ratio
• Modular rings
• Pascal’s triangle
• Binet formula

AMS Classification

• 11B39
• 11B50

References

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