The Periodicity to a Kind of Generalized Collatz Problem

Abstract

The Collatz problem is related to the fixed point problem, and is widely used in mathematics. It has attracted a wide range of math enthusiasts, but is still difficult to solve. So, this article aimed to study the extension of the Collatz problem, more widely, in k-adic. We define a new sequence called Z transformation sequence. Under a suitable assumptions, we can prove that the limit set of the Z transformation sequence must be M={1,2}.