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arXiv · 1903.10096

Convergence of generalized Collatz problem in k-adic field

Yushu Zhu·Sensen Chen·Qing-You Sun
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Abstract

In this article, we define a new k-adic series transformation called Z-transformation and probe into its fixed point and periodicity. We extend the number field of the transform period problem to a wider k-adic field. Different constraints are imposed on k, then different periodic columns are formed after finite Z-transformations. We obtain that their periodic sequences are M1= {1,2} and M2={1,2}\cup {n_0}\cup {n'} respectively after derivation. As an application, it can provide a reference for C problems in more complex algebraic ystems.

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Yushu Zhu, Sensen Chen, Qing-You Sun. 2019-03-25. Convergence of generalized Collatz problem in k-adic field. https://arxiv.org/abs/1903.10096

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