Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZING SOME FIBONACCI-LUCAS RELATIONS

  • Junghyun Hong (Gochon Middle School) ;
  • Jongmin Lee (Hansu Middle School) ;
  • Ho Park (Department of Mathematics Dongguk University)
  • Received : 2022.01.24
  • Accepted : 2022.04.01
  • Published : 2023.01.31
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Abstract

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.

Keywords

Acknowledgement

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.

References

  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