Related papers: Collatz Problem of Positive Integers

This paper has been withdrawn by the author due to the presented idea is wrong.

This paper has been withdrawn due to a crucial theoretical error.

This paper was withdrawn by the authors. The mistake in math.AG/0209223 affects also this paper.

This paper has been withdrawn due to an error, and no further revisions will be made.

This paper has been withdrawn by the author(s), due a crucial error on the entanglement of $\Gamma$ registers.

This paper has been withdrawn by the author because Lemma 3 is incorrect.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This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

I want to withdraw this paper.

This paper is withdrawn because of an error in Lemma 3.1

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn by the author due to some errors.

This paper has been withdrawn by the author due a few mistakes in the paper.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been withdrawn by the author due a crucial error.

This paper has been withdrawn by the author, due to an error in the proof of lemma 7.4. However, numerical evidence strongly suggest that this lemma is true.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.