What question did this study set out to answer?

The aim is to prove the Collatz conjecture by examining the relationship between odd integers.

May 11, 2026Open Access

A Proof of the Collatz Conjecture

Key Points

The aim is to prove the Collatz conjecture by examining the relationship between odd integers.
Analyzed the complete mapping from one odd integer to the next.
Showed that for any odd integer x greater than or equal to 3, the mapping decreases in value.
All trajectories converged into the cycle {4, 2, 1}.
Confirmed the conjecture applies to all odd integers by demonstrating the mapping behavior.

Abstract

We prove the Collatz conjecture by considering the complete map from one odd integer to the next. For any odd x 3, this map strictly decreases the value, forcing all trajectories into the known cycle \4 2 1\.

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Cite This Study

Shengxing He (Sat,) studied this question.

synapsesocial.com/papers/6a0172ac3a9f334c28272e22 https://doi.org/https://doi.org/10.5281/zenodo.20093530

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