Author(s)

Ke Li

Institute of Chemical Industry of Forest Products, CAF, Nanjing, China.

This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number; 2) The odd number must change to a number of LiKe’s second sequence {3ⁿ – 1| n ∈ Z⁺}; 3) Then this 3ⁿ - 1 will change to a smaller 3ⁿ – 1 and gradually decrease to 8 (that is 3² - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2ⁿ (it might even explain 2ⁿ). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.

3x +1 Problem, Collatz-Problem, Collatz Conjecture, LiKe’s Rule, Number Theory

Li, K. (2022) On the Change Rule of 3x + 1 Problem. Journal of Applied Mathematics and Physics, 10, 850-864. doi: 10.4236/jamp.2022.103058.