Displaying similar documents to “Symmetry of iteration graphs”

Tribonacci modulo 2 t and 11 t

Jiří Klaška (2008)

Mathematica Bohemica

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Our previous research was devoted to the problem of determining the primitive periods of the sequences ( G n mod p t ) n = 1 ∞ where ( G n ) 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 .

On the basic character of residue classes.

Peter J. Hilton, Jennifer Hooper, Jean Pedersen (1989)

Publicacions Matemàtiques

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Let t, b be mutually prime positive integers. We say that the residue class t mod b is basic if there exists n such that t ≡ -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy p ≡ 3 mod 4, then t is basic mod b if t is a quadratic non-residue mod p for all such p; and t is not basic mod b if t is a quadratic residue mod p for all such p. If, for all...

Tribonacci modulo p t

Jiří Klaška (2008)

Mathematica Bohemica

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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.