A Modular Theory for the Collatz Conjecture: Convergence and Nonexistence of Infinite Cycles
Abstract
This work develops a Modular Theory for the Collatz Conjecture, focusing on convergence of all positive integers and proving the nonexistence of infinitely diverging cycles. The approach combines modular arithmetic, 2-adic analysis, and dynamics of iterated functions, providing a framework for understanding Collatz orbits in a rigorous way.
Fields of Study & Subjects
Benford’s Law and Fraud Detection
Misinformation and Its Impacts
Probability and Statistical Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 8 January 2026
- Language
- EN
- Document type
- Preprint