Astrophysics

    

Proof of Collatz Conjecture

Authors: Khalid Ibrahim Al-ibraheem

This paper presents a comprehensive and decisive proof of the Collatz conjecture by partitioning the odd integers into three disjoint sets:B,C,D and analyzing their behavior. It then proves the non-existence of non-trivial cycles, and finally applies the conjecture to odd integers starting from the set V=5+12n , demonstrating that all such integers converge to 1.Please refer to v4, as it is clearer and free of typographical errors.

Comments: 18 Pages.

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Submission history

[v1] 2025-10-14 20:45:29
[v2] 2025-10-20 01:28:29 (removed)
[v3] 2025-12-14 07:57:39 (removed)
[v4] 2025-12-28 19:13:59 (removed)
[v5] 2026-02-11 20:56:44

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