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