Korean Journal of Mathematics

  • 제29권4호
  • /
  • Pages.733-740
  • /
  • 2021
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON THE EXTENT OF THE DIVISIBILITY OF FIBONOMIAL COEFFICIENTS BY A PRIME NUMBER

  • Lee, David Taehee (Institude of Science Education for the Gifted and Talented, Yonsei University) ;
  • Lee, Juhyep (Institude of Science Education for the Gifted and Talented, Yonsei University) ;
  • Park, Jinseo (Department of Mathematics Education, Catholic Kwandong University)
  • 투고 : 2021.02.04
  • 심사 : 2021.12.01
  • 발행 : 2021.12.30
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초록

Let (Fn)n≥0 be the Fibonacci sequence and p be a prime number. For 1≤k≤m, the Fibonomial coefficient is defined as $$\[\array{m\\k}\]_F=\frac{F_{m-k+1}{\ldots}{F_{m-1}F_m}}{{F_1}{\ldots}{F_k}}$$ and $\[\array{m\\k}\]_F=0$ whan k>m. Let a and n be positive integers. In this paper, we find the conditions of prime number p which divides Fibonomial coefficient $\[\array{P^{a+n}\\{p^a}}\]_F$. Furthermore, we also find the conditions of p when $\[\array{P^{a+n}\\{p^a}}\]_F$ is not divisible by p.

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과제정보

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2019R1G1A1006396).

참고문헌

  1. G. Fontene, Geneeralisation d'une formule connue, Nouv. Ann. Math 4 (15), (1915), 112
  2. T. Lengyel, The order of the Fibonacci and Lucas numbers, Fibonacci Quart. 33 (3) (1995), 184-240
  3. D. Margues, J. Sellers, and P. Trojovske, On divisibility properties of certain Fibonomial coefficients by a prime p, Fibonacci Quart. 51 (2013), 78-83