A NON-Proof of the Non-Existence of Non-Trivial Collatz Cycles

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Authors: Nathaniel Benjamin Helms
Cited by: 0

Abstract

This 'proof' is broken. Nevertheless, it contains a fascinating exploration of an m-structure for the accumulation of "+1" terms in a Collatz sequence. The divisibility constraints the cycle hypothesis puts on the terms is stupendous. Unfortunately, all conventional approaches to show a modular contradiction lead only to tautologies and forks. Good luck to all who attempt to find the contradiction. I am returning to my efforts to prve the conjecture "all at once". I will publish those beautiful structures at some point, whether I succeed or not.

Fields of Study & Subjects

Benford’s Law and Fraud Detection Probability and Statistical Research Genetics Bioinformatics and Biomedical Research

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
6 January 2026