[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2021.34.4.327

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)

Publication Information

Journal of the Chungcheong Mathematical Society / v.34, no.4, 2021 , pp. 327-334 More about this Journal

Abstract

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.

Keywords

Diophantine m-tuple; Fibonacci numbers; Pell equation;

Citations & Related Records

Reference

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.