Number Theory

    

An Algebraic Reformulation of the Collatz Map as a Modular Operation on Consecutive Integers

Authors: Rayan Bhuttoo

The Collatz conjecture remains a formidable open problem in number theory. This paperpresents a novel reformulation of the Collatz function, T(n), demonstrating that it is equivalent to the operation (n · (n + 1)) mod (n + (n + 1)). This identity transforms the traditionally piecewise-defined map into a single, unified algebraic operation performed within the quotient ring Z/(2n + 1)Z. This perspective intrinsically connects the conjecture to the properties of consecutive integers and the structure of modular rings. Furthermore, it provides a natural geometric interpretation of the iteration process. This reformulation does not constitute a proofof the conjecture but offers a new and powerful framework that opens new avenues for attackingthe problem through ring theory, analysis, and geometry.

Comments: 6 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Download: PDF

Submission history

[v1] 2025-08-31 20:19:11

Unique-IP document downloads: 180 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