Geodesic
Tribonacci modulo $2^t$ and $11^t$
Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 377-387

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Our previous research was devoted to the problem of determining the primitive periods of the sequences $(G_n\mod p^t)_{n=1}^{\infty }$ where $(G_n)_{n=1}^{\infty }$ is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime $p\ne 2,11$. In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes $p=2,11$.
Our previous research was devoted to the problem of determining the primitive periods of the sequences $(G_n\mod p^t)_{n=1}^{\infty }$ where $(G_n)_{n=1}^{\infty }$ is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime $p\ne 2,11$. In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes $p=2,11$.
DOI : 10.21136/MB.2008.140627
Classification : 11B39, 11B50
Keywords: Tribonacci; modular periodicity; periodic sequence 
Klaška, Jiří. Tribonacci modulo $2^t$ and $11^t$. Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 377-387. doi: 10.21136/MB.2008.140627
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[1] Klaška, J.: Tribonacci modulo $p^t$. Math. Bohem. 133 (2008), 267-288. | MR

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

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

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