Article
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Proof the Collatz Conjecture by a new view of natural numbers
Version 1
: Received: 16 September 2023 / Approved: 18 September 2023 / Online: 19 September 2023 (08:07:22 CEST)
How to cite: Feng, J. Proof the Collatz Conjecture by a new view of natural numbers. Preprints 2023, 2023091200. https://doi.org/10.20944/preprints202309.1200.v1 Feng, J. Proof the Collatz Conjecture by a new view of natural numbers. Preprints 2023, 2023091200. https://doi.org/10.20944/preprints202309.1200.v1
Abstract
The two main strategies used in this study are the binary representation and the decomposition of a natural number into many compound functions of odd function and even function. The Collatz conjecture regarding odd even numbers in number theory can be examined and discussed using them in this way: The sequence created by the finite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 85 years.
Keywords
binary representation; composite function; Collatz conjecture; ultimately periodic sequence; chaos
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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