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Tribonacci; modular periodicity; periodic sequence
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 $p=2,11$.
[1] Klaška, J.: Tribonacci modulo $p^t$. Math. Bohem. 133 (2008), 267-288. MR 2494781
[2] Vince, A.: Period of a linear recurrence. Acta Arith. 39 (1981), 303-311. DOI 10.4064/aa-39-4-303-311 | MR 0640918 | Zbl 0396.12001
[3] Waddill, M. E.: Some properties of a generalized Fibonacci sequence modulo $m$. The Fibonacci Quarterly 16 (Aug. 1978) 344-353. MR 0514322 | Zbl 0394.10007
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