Number Theory

    

Collatz Conjecture: The Proof

Authors: Leszek Mazurek

In this paper, we prove the Collatz conjecture. The proof consists of two parts. The first, shows that the Collatz conjecture is the equivalent of the statement that every positive integer can be presented as a certain equation. In the second part, we prove that for every initial positive integer, this equation can be found. To achieve this, we propose a procedure that can be iterated, and we prove that by doing this we arrive at this equation. We also prove that any initial positive integer can be presented in an infinite number of ways in the form of needed equation. Each such form represents the loop occurring when number 1 is reached. The analysis is conducted using binary representation of numbers.

Comments: Pages.

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Submission history

[v1] 2021-05-02 10:41:39
[v2] 2021-08-07 16:44:02
[v3] 2021-08-22 17:46:30
[v4] 2021-09-05 14:34:32
[v5] 2021-09-24 13:39:38

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