Around the Fibonacci Numeration System

Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.

Grantor dc:publisher

University of North Texas

Year dc:date

2007

Author dc:creator

• Edson, Marcia Ruth

Contributors dc:contributor

• Zamboni, Luca
• Cherry, William, 1966-
• Richter, Olav

• numeration systems
• positive integer
• Fibonacci sequence
• Fibonacci numbers.
• Fine and Wilf theorem
• general and Euclidian algorithms

Statement dc:rights

• Public
• Copyright
• Edson, Marcia Ruth
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 179921850
https://digital.library.unt.edu/ark:/67531/metadc3676/
ark: ark:/67531/metadc3676

OAI identifier oai:identifier

info:ark/67531/metadc3676