Detailed Information
Cited 5 time in 
Cited 7 time in 
Cited 7 time in
Metadata Downloads
Representation of Integers as Sums of Fibonacci and Lucas Numbersopen access
- Authors
- Park, Ho; Cho, Bumkyu; Cho, Durkbin; Cho, Yung Duk; Park, Joonsang
- Issue Date
- Oct-2020
- Publisher
- MDPI
- Keywords
- Fibonacci numbers; Lucas numbers; Zeckendorf's theorem
- Citation
- SYMMETRY-BASEL, v.12, no.10, pp 1 - 8
- Pages
- 8
- Indexed
- SCIE
SCOPUS
- Journal Title
- SYMMETRY-BASEL
- Volume
- 12
- Number
- 10
- Start Page
- 1
- End Page
- 8
- ISSN
- 2073-8994
2073-8994
- Abstract
- Motivated by the Elementary Problem B-416 in the Fibonacci Quarterly, we show that, given any integers n and r with n >= 2, every positive integer can be expressed as a sum of Fibonacci numbers whose indices are distinct integers not congruent to r modulo n. Similar expressions are also dealt with for the case of Lucas numbers. Symmetric and anti-symmetric properties of Fibonacci and Lucas numbers are used in the proofs.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Natural Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
Related Researcher
- Cho, Durk Bin
- College of Natural Science (Department of Mathematics)