Article
Version 2
Preserved in Portico This version is not peer-reviewed
Proof of the Collatz Conjecture
Version 1
: Received: 25 October 2022 / Approved: 27 October 2022 / Online: 27 October 2022 (10:58:37 CEST)
Version 2 : Received: 29 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (09:24:48 CET)
Version 3 : Received: 14 November 2022 / Approved: 15 November 2022 / Online: 15 November 2022 (10:59:46 CET)
Version 4 : Received: 3 September 2023 / Approved: 4 September 2023 / Online: 6 September 2023 (10:27:26 CEST)
Version 2 : Received: 29 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (09:24:48 CET)
Version 3 : Received: 14 November 2022 / Approved: 15 November 2022 / Online: 15 November 2022 (10:59:46 CET)
Version 4 : Received: 3 September 2023 / Approved: 4 September 2023 / Online: 6 September 2023 (10:27:26 CEST)
A peer-reviewed article of this Preprint also exists.
Sukuşu, B. (2022). Proof of the Collatz conjecture. Theor Math Appl. Sukuşu, B. (2022). Proof of the Collatz conjecture. Theor Math Appl.
Abstract
Collatz conjecture (or 3n+1 problem) has been explored for about 85 years. In this article, we prove the Collatz conjecture. We will show that this conjecture is valid for all positive integers by performing the Collatz inverse operation on the numbers that comply with the rules of the Collatz conjecture. Finally, it will be proved that there are no positive integers that do not comply with this conjecture.
Keywords
Collatz operation; Collatz inverse operation and Collatz numbers
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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Commenter: Bülent Sukuşu
Commenter's Conflict of Interests: Author
2 The Conjecture and (Releated) Related Conversions
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Commenter's Conflict of Interests: I am one of the author