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Collatz Conjecture Proof and General Equation
Version 1
: Received: 10 April 2024 / Approved: 11 April 2024 / Online: 11 April 2024 (07:07:56 CEST)
How to cite: Hahn, K.O. Collatz Conjecture Proof and General Equation. Preprints 2024, 2024040778. https://doi.org/10.20944/preprints202404.0778.v1 Hahn, K.O. Collatz Conjecture Proof and General Equation. Preprints 2024, 2024040778. https://doi.org/10.20944/preprints202404.0778.v1
Abstract
A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.
Keywords
collatz conjecture; proof; rules; dendritic pathway
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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