Displaying similar documents to “On some Markov matrices arising from the generalized Collatz mapping”

Some Borel measures associated with the generalized Collatz mapping

K. Matthews (1992)

Colloquium Mathematicae

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This paper is a continuation of a recent paper [2], in which the authors studied some Markov matrices arising from a mapping T:ℤ → ℤ, which generalizes the famous 3x+1 mapping of Collatz. We extended T to a mapping of the polyadic numbers ℤ ^ and construct finitely many ergodic Borel measures on ℤ ^ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.

On Obláth's problem.

Gica, Alexandru, Panaitopol, Laurenţiu (2003)

Journal of Integer Sequences [electronic only]

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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...