Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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. (2023). Proof of the Collatz conjecture. Theor Math Appl. Sukuşu, B. (2023). 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

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