What question did this study set out to answer?

The aim is to establish the Collatz conjecture as a proven theorem, resolving its status in mathematics.

August 2, 2026Open Access

proof of Collatz conjecture - Theorem

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The aim is to establish the Collatz conjecture as a proven theorem, resolving its status in mathematics.
Utilized mathematical logic and proof techniques.
Identified and corrected simplifications in initial attempts.
Clarified the inductive step to ensure accuracy.
Collatz conjecture has been successfully proven as a theorem.
Previous errors in simplification were rectified in Version 2.
Introduced rigorous proof techniques to solidify the argument.

Implication

Theorem proves Collatz conjecture, marking a significant mathematical breakthrough.

Abstract

Collatz conjecture is now proven. It was first introduced by German mathematician Lothar Collatz in 1937.It is not a conjecture anymore but a proven Theorem.Note: please read Version 2 becuase there was a mistake of simplification in LaTex in Version 1, inductive step of n+1: = 2·{3}[{2(22L-2 - 1)}{{3}}] + 4

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Cite This Study

Ismail (Ari Khusraw) Mostafanejad (2026) studied this question.

synapsesocial.com/papers/6a6eeaa21b0468a7eeab2e77 https://doi.org/10.5281/zenodo.21698600

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Implication

Theorem proves Collatz conjecture, marking a significant mathematical breakthrough.

proof of Collatz conjecture - Theorem

Key Points

Implication

Abstract

Discussion

Cite This Study

proof of Collatz conjecture - Theorem

Key Points

Implication

Abstract

Discussion

Cite This Study

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