충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제34권4호
  • /
  • Pages.327-334
  • /
  • 2021
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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FIBONACCI SEQUENCES IN kTH POWER RESIDUES

  • Chung, Youchan (Institude of Science Education for the Gifted and Talented Yonsei University) ;
  • Jang, Eunyool (Institude of Science Education for the Gifted and Talented Yonsei University) ;
  • Park, Jinseo (Department of Mathematics Education Catholic Kwandong University) ;
  • Park, Sanghoon (Institude of Science Education for the Gifted and Talented Yonsei University)
  • 투고 : 2021.10.27
  • 심사 : 2021.11.30
  • 발행 : 2021.11.15
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초록

In this paper, we find all the prime numbers p that satisfy the following statement. If a positive integer k is a divisor of p - 1, then there is a sequence consisting of all k-th power residues modulo p, satisfying the recurrence equation of the Fibonacci sequence modulo p.

키워드

과제정보

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

참고문헌

  1. A. Gica, Quaderatic Residues In Fibonacci Sequences, Fibonacci Quart., 46/47 (2008/2009), 68-72.
  2. A. Gica and L. Panaitopol, O Introducere n Aritmetic i Teoria Numerelor, Bucharest University Press, Bucharest, 2001.