Remer, M. (2023) A Comparative Analysis of the New-3(-n)-1 Remer Conjecture and a Proof of the 3n+1 Collatz Conjecture. Journal of Applied Mathematics and Physics, 11, 2216-2220.
https://doi.org/10.4236/jamp.2023.118143

has been cited by the following article:

• TITLE: Base-X Conjecture and Collatz Conjecture Proof

  AUTHORS: Sheng Zhao

  KEYWORDS: Collatz Conjecture, Base-X Conjecture, Collatz Spiral, Collatz Ring, Collatz Tree

  JOURNAL NAME: Applied Mathematics, Vol.16 No.4, April 28, 2025

  ABSTRACT: A new Base-X Conjecture was introduced in this paper, and Collatz Conjecture is just one case of Base-X Conjecture - Base-3 (Ternary). Based on Base-X number system property and Collatz Conjecture iteration, it has been proved that for any positive integer D, there are n and m which exist for D n + Y n = 2 m . D n + Y n is just the result built up by collecting divided by 2 of Collatz Conjecture iteration. Divided by 2m will make the Collatz Conjecture get a result of 1 for any positive integer. Also, the Collatz Tree showed that for any odd positive number, there is only one route existing in the Collatz Tree down to 1 on Collatz Conjecture iteration.