Advances in Pure Mathematics

Volume 12, Issue 1 (January 2022)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

Google-based Impact Factor: 0.48  Citations  

The Proof of the 3X + 1 Conjecture

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DOI: 10.4236/apm.2022.121002    1,321 Downloads   18,598 Views  Citations

ABSTRACT

In this paper, we use two new effective tools and ingenious methods to prove the 3X + 1 conjecture. By using the recursive method, we firstly prove that any positive integer can be turned into an element of fourth column of the infinite-row-six-column-matrix after a finite times operation, thus we convert “the 3X + 1 conjecture” into an equivalent conjecture, which is: Any positive integer n must become 1 after finite operations under formation of σ(n) , where Then, with the help of the infinite-row-four-column-matrix, we continue to use the recursive method to prove this conjecture strictly.

Share and Cite:

Wang, M. , Yang, Y. , He, Z. and Wang, M. (2022) The Proof of the 3X + 1 Conjecture. Advances in Pure Mathematics, 12, 10-28. doi: 10.4236/apm.2022.121002.

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