Representation of integers as sums of fibonacci and lucas numbers

Ho Park, Bumkyu Cho, Durkbin Cho, Yung Duk Cho, Joonsang Park

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Article number1625
Pages (from-to)1-8
Number of pages8
JournalSymmetry
Volume12
Issue number10
DOIs
StatePublished - Oct 2020

Keywords

  • Fibonacci numbers
  • Lucas numbers
  • Zeckendorf’s theorem

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