Impossibility of Diverging Cycles in the Collatz Conjecture

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Alfonso Buesa Estallo
DOI: 10.5281/zenodo.18289916
Cited by: 0

Abstract

The article demonstrates that no positive integer can indefinitely evade the modular regularities of the Collatz conjecture, proving through 2-adic analysis that the exceptional set \( E \) is empty, thereby ruling out the existence of cycles that diverge to infinity.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories Mathematical Dynamics and Fractals

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
18 January 2026
Document type
Preprint