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

Klaška, Jiří

Math. Bohem. 133, No. 4, 377-387 (2008).

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