Number Theory

    

A Deductive Justification for The Collatz Conjecture

Authors: Christian I. G. Winsor

This paper presents a new approach to understanding the Collatz Conjecture. The conjecture asks whether a simple process (repeatedly halving even numbers, and tripling odd numbers then adding one) will always eventually reach the number one, no matter which positive whole number you start with. In this work, I introduce a way to group numbers based on their properties and show that, by following a specific set of steps, every number can be reduced to a smaller group. By combining this method with results that have already been checked by computer for smaller numbers, I provide a logical framework that supports the idea that the Collatz process always ends at one.

Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Download: PDF

Submission history

[v1] 2025-04-27 20:05:31

Unique-IP document downloads: 600 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus