Geodesic
Tribonacci modulo $p^t$
Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 267-288

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MR Zbl
Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus $p$ and by its powers $p^t$, which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.
Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus $p$ and by its powers $p^t$, which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.
DOI : 10.21136/MB.2008.140617
Classification : 11B39, 11B50
Keywords: Tribonacci; modular periodicity; periodic sequence 
Klaška, Jiří. Tribonacci modulo $p^t$. Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 267-288. doi: 10.21136/MB.2008.140617
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[1] Elia, M.: Derived sequences, the Tribonacci recurrence and cubic forms. The Fibonacci Quarterly 39.2 (2001), 107-115. | MR | Zbl

[2] Klaška, J.: Tribonacci modulo $2^t$ and $11^t$. (to appear) in Math. Bohem.

[3] Klaška, J.: Tribonacci partition formulas modulo $m$. Preprint (2007). | MR

[4] Sun, Z.-H., Sun, Z.-W.: Fibonacci numbers and Fermat's last theorem. Acta Arith. 60 (1992), 371-388. | DOI | MR | Zbl

[5] Vince, A.: Period of a linear recurrence. Acta Arith. 39 (1981), 303-311. | DOI | MR | Zbl

[6] Waddill, M. E.: Some properties of a generalized Fibonacci sequence modulo $m$. The Fibonacci Quarterly 16 4 (Aug. 1978) 344-353. | MR | Zbl

[7] Wall, D. D.: Fibonacci series modulo $m$. Amer. Math. Monthly 67 6 (1960), 525-532. | DOI | MR | Zbl

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