Tribonacci modulo $2^t$ and $11^{t}$

Abstract: 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 $p\ne2,11$. In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes $p=2,11$.

Keywords: Tribonacci, modular periodicity, periodic sequence

Classification (MSC2000): 11B50, 11B39

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