Proof of the Collatz Conjecture
Abstract
The Collatz Conjecture (or 3n+1 problem) has been explored for about 86years. In this article, we prove the Collatz Conjecture. We will show thatthis conjecture holds for all positive integers by applying the Collatz inverseoperation to the numbers that satisfy the rules of the Collatz Conjecture.Finally, we will prove that there are no positive integers that do not satisfythis conjecture.
Fields of Study & Subjects
Benford’s Law and Fraud Detection
Probability and Statistical Research
Computational Physics and Python Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 January 2026