Number Theory

    

Proof of the Collatz Conjecture for the Natural Numbers

Authors: Daniel Gerrad Boyle

This document proves that the Collatz Conjecture is true for the Natural numbers excluding zero. Use is made of the probability distribution of even and odd numbers in supposed diverging Collatz sequences to establish that Collatz sequences do not diverge, having a finite number of terms, and are bounded. Finally proof by contradiction, the pigeon hole principle and proof by induction are used to prove that the Collatz Conjecture is true via two theorems.

Comments: 20 Pages.

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Submission history

[v1] 2024-10-29 02:33:28
[v2] 2024-11-12 06:51:29
[v3] 2024-12-03 21:40:38

Unique-IP document downloads: 1195 times

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