TITLE:
The Proof of the 3X + 1 Conjecture
AUTHORS:
Maoze Wang, Yongbao Yang, Zhenxiang He, Meiyi Wang
KEYWORDS:
The 3X + 1 Conjecture, (Z+)∞x6, (Z+)∞x4, Transformation, Module
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.1,
January
26,
2022
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.