대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
  • /
  • Pages.89-96
  • /
  • 2023
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

GENERALIZING SOME FIBONACCI-LUCAS RELATIONS

  • Junghyun Hong (Gochon Middle School) ;
  • Jongmin Lee (Hansu Middle School) ;
  • Ho Park (Department of Mathematics Dongguk University)
  • 투고 : 2022.01.24
  • 심사 : 2022.04.01
  • 발행 : 2023.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin-Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.

키워드

과제정보

H. Park was supported by the National Research Foundation of Korea (NRF-2019R1C1C1010211). This research was partially supported by KAIST (Global Institute For Talented Education) and Dongguk University Science Education Institute for the Gifted, Korea Foundation for the Advancement of Science and Creativity financed by the Ministry of Science and ICT and the Ministry of Economy and Finance.

참고문헌

  1. A. T. Benjamin and J. J. Quinn, Fibonacci and Lucas identities through colored tilings, Util. Math. 56 (1999), 137-142.
  2. S. D. Dafnis, On the relation between Fibonacci and Lucas numbers, Fibonacci Quart. 58 (2020), no. 5, 111-114.
  3. T. Edgar, Extending some Fibonacci-Lucas relations, Fibonacci Quart. 54 (2016), no. 1, 79.
  4. T. Koshy, Fibonacci and Lucas Numbers with Applications. Vol. 2, Pure and Applied Mathematics (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2019.
  5. D. Marques, A new Fibonacci-Lucas relation, Amer. Math. Monthly 122 (2015), no. 7, 683. https://doi.org/10.4169/amer.math.monthly.122.7.683