In this paper we find certain equivalent formulations of Wall's question and derive two interesting criteria that can be used to resolve this question for particular primes.
Our previous research was devoted to the problem of determining the primitive periods of the sequences (Gn mod p t )∞ n=1 where (Gn)∞ n=1 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 ≠ 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 research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus p and by its powers p t , which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers.