Number Theory

    

Proof of the Collatz Conjecture

Authors: Wiroj Homsup, Nathawut Homsup

The Collatz conjecture considers recursively sequences of positive integers where n is succeeded by n/2 , if n is even, or (3n+1)/2 , if n is odd. The conjecture states that for all starting values n the sequence eventually reaches the trivial cycle 1, 2, 1, 2u2026u2026The inverted Collatz sequences can be represented as a tree with 1 as its root node. In order to prove the Collatz conjecture, one must demonstrate that the tree covers all positive integers. In this paper, we construct a Collatz tree with 1 as its root node by connecting infinite number of basic trees. Each basic tree relates to each positive integers. We prove that a Collatz tree is a connected tree and covers all positive integers.

Comments: 9 Pages.

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Submission history

[v1] 2023-11-22 21:58:46
[v2] 2024-09-04 20:22:22

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