Volume no :23, Issue no: 1, December (2020)

CONVERGENCE OF GENERALIZED COLLATZ PROBLEM IN k-ADIC FIELD

Author's: Yushu Zhu, Sensen Chen and Qing-You Sun
Pages: [33] - [47]
Received Date: September 12, 2020
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100122154

Abstract

In this article, we define a new series transformation called transformation and probe into its fixed point and periodicity. We extend the number field of the transform period problem to a wider field. Different constraints are imposed on then different periodic columns are formed after finite transformations. We obtain that their periodic sequences are and respectively after derivation. As an application, it can provide a reference for C problems in more complex algebraic systems.

Keywords

Collatz problem, mathematical induction, fixed point.