Preprint Article Version 9 Preserved in Portico This version is not peer-reviewed

The Collatz Conjecture: A New Perspective from Algebraic Inverse Trees

Version 1 : Received: 11 October 2023 / Approved: 12 October 2023 / Online: 12 October 2023 (04:43:40 CEST)
Version 2 : Received: 13 October 2023 / Approved: 13 October 2023 / Online: 13 October 2023 (04:48:03 CEST)
Version 3 : Received: 13 October 2023 / Approved: 17 October 2023 / Online: 17 October 2023 (10:26:40 CEST)
Version 4 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 18 October 2023 (10:09:49 CEST)
Version 5 : Received: 19 October 2023 / Approved: 20 October 2023 / Online: 20 October 2023 (10:28:38 CEST)
Version 6 : Received: 21 October 2023 / Approved: 23 October 2023 / Online: 23 October 2023 (10:35:42 CEST)
Version 7 : Received: 26 October 2023 / Approved: 26 October 2023 / Online: 27 October 2023 (09:14:36 CEST)
Version 8 : Received: 28 October 2023 / Approved: 30 October 2023 / Online: 30 October 2023 (09:38:23 CET)
Version 9 : Received: 30 October 2023 / Approved: 31 October 2023 / Online: 31 October 2023 (11:01:44 CET)
Version 10 : Received: 1 November 2023 / Approved: 2 November 2023 / Online: 2 November 2023 (08:16:04 CET)
Version 11 : Received: 8 November 2023 / Approved: 8 November 2023 / Online: 8 November 2023 (07:53:02 CET)
Version 12 : Received: 21 November 2023 / Approved: 22 November 2023 / Online: 24 November 2023 (04:11:49 CET)
Version 13 : Received: 27 December 2023 / Approved: 28 December 2023 / Online: 29 December 2023 (01:14:06 CET)
Version 14 : Received: 16 March 2024 / Approved: 17 March 2024 / Online: 18 March 2024 (10:42:38 CET)
Version 15 : Received: 24 March 2024 / Approved: 25 March 2024 / Online: 26 March 2024 (11:50:16 CET)
Version 16 : Received: 28 March 2024 / Approved: 28 March 2024 / Online: 29 March 2024 (11:23:27 CET)
Version 17 : Received: 30 March 2024 / Approved: 1 April 2024 / Online: 2 April 2024 (11:53:22 CEST)
Version 18 : Received: 28 April 2024 / Approved: 29 April 2024 / Online: 29 April 2024 (09:46:13 CEST)

A peer-reviewed article of this Preprint also exists.

Diedrich, E. The Collatz Conjecture: A New Proof Using Algebraic Inverse Tree. International Journal of Pure and Applied Mathematics Research 2024, 4, 34–79, doi:10.51483/ijpamr.4.1.2024.34-79. Diedrich, E. The Collatz Conjecture: A New Proof Using Algebraic Inverse Tree. International Journal of Pure and Applied Mathematics Research 2024, 4, 34–79, doi:10.51483/ijpamr.4.1.2024.34-79.

Abstract

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

Keywords

collatz cojecture; algebraic inverse trees; formal proof of collatz conjecture

Subject

Computer Science and Mathematics, Mathematics

Comments (1)

Comment 1
Received: 31 October 2023
Commenter: Eduardo Diedrich
Commenter's Conflict of Interests: Author
Comment: Finally, a formal proof of the conjecture is given. Non-central sections were removed and more relevant ones were added.
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