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Representation of Integers as Sums of Fibonacci and Lucas Numbers
- Park, Ho;
- Cho, Bumkyu;
- Cho, Durkbin;
- Cho, Yung Duk;
- Park, Joonsang
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7초록
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.
키워드
Fibonacci numbers; Lucas numbers; Zeckendorf's theorem; TRANSMISSION
- 제목
- Representation of Integers as Sums of Fibonacci and Lucas Numbers
- 저자
- Park, Ho; Cho, Bumkyu; Cho, Durkbin; Cho, Yung Duk; Park, Joonsang
- 발행일
- 2020-10
- 유형
- Article
- 저널명
- Symmetry
- 권
- 12
- 호
- 10
- 페이지
- 1 ~ 8