## Tribonacci modulo $$2^t$$ and $$11^t$$.(English)Zbl 1174.11022

Summary: Our previous research was devoted to the problem of determining the primitive periods of the sequences $$(G_n\bmod {p^t})_{n=1}^{\infty }$$ 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 $$p\neq 2,11$$. In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes $$p=2,11$$.

### MSC:

 11B50 Sequences (mod $$m$$) 11B39 Fibonacci and Lucas numbers and polynomials and generalizations

### Keywords:

Tribonacci; modular periodicity; periodic sequence
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