Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed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)

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

Comments (1)

Comment 1
Received: 6 September 2023
Commenter: Bülent Sukuşu
Commenter's Conflict of Interests: Author
Comment: language corrections
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