Article
Version 4
Preserved in Portico This version is not peer-reviewed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
The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture. Finally, we will prove that there are no positive integers that do not satisfy this conjecture.
Keywords
Collatz operation; Collatz inverse operation; 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.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Bülent Sukuşu
Commenter's Conflict of Interests: Author