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 language | English |
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Article number | 1625 |
Pages (from-to) | 1-8 |
Number of pages | 8 |
Journal | Symmetry |
Volume | 12 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2020 |
Keywords
- Fibonacci numbers
- Lucas numbers
- Zeckendorf’s theorem