Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

A Solution of The Collatz Conjecture Problem

Version 1 : Received: 30 January 2023 / Approved: 30 January 2023 / Online: 30 January 2023 (06:21:02 CET)
Version 2 : Received: 11 February 2023 / Approved: 13 February 2023 / Online: 13 February 2023 (02:53:06 CET)
Version 3 : Received: 4 March 2023 / Approved: 6 March 2023 / Online: 6 March 2023 (04:14:16 CET)
Version 4 : Received: 11 March 2023 / Approved: 13 March 2023 / Online: 13 March 2023 (03:05:38 CET)
Version 5 : Received: 28 March 2023 / Approved: 28 March 2023 / Online: 28 March 2023 (05:32:08 CEST)
Version 6 : Received: 3 April 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (07:22:34 CEST)
Version 7 : Received: 10 April 2023 / Approved: 11 April 2023 / Online: 11 April 2023 (03:28:27 CEST)
Version 8 : Received: 22 June 2023 / Approved: 25 June 2023 / Online: 25 June 2023 (04:40:44 CEST)
Version 9 : Received: 20 July 2023 / Approved: 21 July 2023 / Online: 21 July 2023 (08:53:32 CEST)
Version 10 : Received: 10 August 2023 / Approved: 10 August 2023 / Online: 11 August 2023 (03:01:11 CEST)
Version 11 : Received: 19 September 2023 / Approved: 20 September 2023 / Online: 21 September 2023 (03:25:23 CEST)
Version 12 : Received: 14 October 2023 / Approved: 17 October 2023 / Online: 17 October 2023 (07:08:50 CEST)
Version 13 : Received: 28 October 2023 / Approved: 30 October 2023 / Online: 30 October 2023 (09:47:16 CET)
Version 14 : Received: 19 November 2023 / Approved: 21 November 2023 / Online: 21 November 2023 (10:43:13 CET)

How to cite: duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v3 duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v3

Abstract

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, and get a solution for this equation, which is exactly same with that got from calculating directly. Then give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the even and odd sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build another complement weight function model, prove it increase to its convergence state. Indicate that this kind of iteration calculation has determined direction, and gradually regularly converges.

Keywords

collatz conjecture; (*3+2^m-1)/2^k odd sequence,weight function

Subject

Computer Science and Mathematics, Algebra and Number Theory

Comments (1)

Comment 1
Received: 6 March 2023
Commenter: baoyuan duan
Commenter's Conflict of Interests: Author
Comment: build a (*3+2^m-1)/2^k tree model, use math induction to prove it can converge.
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