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- Title
Representation of Integers as Sums of Fibonacci and Lucas Numbers.
- Authors
Park, Ho; Cho, Bumkyu; Cho, Durkbin; Cho, Yung Duk; Park, Joonsang
- 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.
- Subjects
LUCAS numbers; INTEGERS
- Publication
Symmetry (20738994), 2020, Vol 12, Issue 10, p1625
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym12101625