Number Theory


Collatz Conjecture Proof

Authors: James Edwin Rock

Collatz sequences are formed by applying the Collatz algorithm to any positive integer. If it is even repeatedly divide by two until it is odd, then multiply by three and add one to get an even number and vice versa. If the Collatz conjecture is true eventually you always get back to one. A connected Collatz Structure is created, which contains all positive integers exactly once. The terms of the Collatz Structure are joined together via the Collatz algorithm. Thus, every positive integer forms a Collatz sequence with unique terms terminating in the number one.

Comments: 12 Pages.

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Submission history

[v1] 2019-01-16 12:07:43
[v2] 2019-01-17 08:32:12
[v3] 2019-01-29 11:21:03
[v4] 2019-02-21 08:01:40
[v5] 2019-02-25 10:42:27
[v6] 2019-03-18 08:58:13
[v7] 2019-04-24 09:30:58 (removed)
[v8] 2019-05-02 10:36:14
[v9] 2019-06-20 11:56:51
[vA] 2019-08-12 12:39:07
[vB] 2019-08-16 14:27:09

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