# 证明角谷猜想是正确的Proof of Collatz Conjecture

DOI: 10.12677/PM.2019.93055, PDF, HTML, XML, 下载: 401  浏览: 1,010

Abstract: Assume that Collatz conjecture is incorrect, and represent the set of natural numbers as N, then the N set can be divided into B set and H set. Set B satisfies the Collatz conjecture; set H does not satisfy the Collatz conjecture. After performing the Collatz operation on the number in the H, it proves that the Collatz conjecture is correct.

1. 预备工作

1) 满足角谷猜想的自然数，记为集合B

$\text{B}=\left\{{b}_{1},{b}_{2},{b}_{3},{b}_{4},\cdots ,{b}_{i}\right\}$, ${b}_{1}=1,{b}_{2}=2,{b}_{3}=3,{b}_{4}=4,{b}_{i}\to \infty$

2) 不满足角谷猜想的自然数称为非角谷数集，记为集合H

$\text{H}=\left\{{h}_{1},{h}_{2},{h}_{3},{h}_{4},\cdots ,{h}_{i}\right\}$

2. 命题证明

Figure 1. Line $X=3Y+1$ intersects Line $Y={h}_{i}$

${h}_{i+1}=\frac{{\left(3{h}_{1}+1\right)}^{i}}{{h}_{1}^{i-1}{2}^{{n}_{1}+{n}_{2}+\cdots +{n}_{i}}}$, $\left({n}_{1}+{n}_{2}+\cdots +{n}_{i}\right)\ge i$ , (1)

${n}_{1}={n}_{2}=\cdots ={n}_{i}=1$ 时， $\left({n}_{1}+{n}_{2}+\cdots +{n}_{i}\right)=i$，设 $\left({n}_{1}+{n}_{2}+\cdots +{n}_{i}\right)=\beta ,\beta \ge i$

NOTES

 [1] Gu, C.H. (1992) Mathematics Dictionary. Shanghai Dictionary Press, Shanghai. [2] Min, S.H. (1981) Method of Number Theory. Science Press, Beijing.