Proof the Collatz Conjecture by a new view of natural numbers

Jishe Feng

doi:10.20944/preprints202309.1200.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 September 2023 / Approved: 18 September 2023 / Online: 19 September 2023 (08:07:22 CEST)

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.

binary representation; composite function; Collatz conjecture; ultimately periodic sequence; chaos

Computer Science and Mathematics, Algebra and Number Theory

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Proof the Collatz Conjecture by a new view of natural numbers

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