Periods of Fibonacci Functions Modulo m

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Nattaporn Thongngam
Ronnason Chinram


 A Fibonacci function is a function f: Z → Z such that f(x+2) = f(x+1) + f(x) for all x∈Z. A Fibonacci function is a generalization of the Fibonacci sequence and Lucas sequence. The purpose of this research is to study periods of Fibonacci functions modulo m and connect to the period of the Fibonacci sequence and Lucas sequence modulo m


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[1] Koshy, T. (2001). Fibonacci and Lucas Number with Applications. New Jersey: John Wiley & Sons, Inc.

[2] Jisawat, K., & Jitpitak, S. (2552). Some Divisibility Properties of Fibonacci Numbers. Thaksin University Journal, 12(2), 50-58.

[3] Wiboonton, K. (2560). The Fibonacci Sequence in Mathematics Courses. Math Journal, 62(691), 1-11.

[4] Carlitz, L., & Ferns, H. H. (1970). Some Fibonacci and Lucas Identities. Fibonacci Quarterly, 8, 61-73.

[5] Luca, F. (2003). Fibonacci and Lucas Numbers with only One Distinct Digit. Portugaliae Mathematica, 57(2), 243-254.

[6] Elmore, M. (1967). Fibonacci Functions. Fibonacci Quarterly, 5, 371-382.

[7] Bunder, M. W. (1978). More Fibonacci Functions. Fibonacci Quarterly, 16, 97-98.

[8] Spickerman, W. R. (1970). A Note on Fibonacci Functions. Fibonacci Quarterly, 8, 397-401.

[9] Jameson, G. J. O. (2018). Fibonacci Periods and Multiples. Mathematical Gazette, 102(553), 63-76.