Related papers: Collatz Problem of Positive Integers

This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author, due to a crucial error in page 5.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author due to its publication

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2

This paper has been withdrawn by the author, due an error in claim 1.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn by the author due to a error in attachment of source file.

This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.

This paper has been withdrawn by the author(s), due a mistake of factor 1/2.

The paper was withdrawn by the author. It contained various errors.

The paper has been withdrawn by the author due to a crucial error.

This paper is withdrawn. We found a mistake in Lemma 4.1

This paper has been withdrawn by the author due to a crucial error in the submission action.