The Periodicity to a Kind of Generalized Collatz Problem

Sensen Chen; Qing-You Sun; Yushu Zhu

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arXiv · 1903.03365

The Periodicity to a Kind of Generalized Collatz Problem

Sensen Chen·Qing-You Sun·Yushu Zhu

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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}.

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Sensen Chen, Qing-You Sun, Yushu Zhu. 2019-03-08. The Periodicity to a Kind of Generalized Collatz Problem. https://arxiv.org/abs/1903.03365

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