A New Way to Proof 3x+1 Problem

TL;DR

This paper proposes a novel classification of numbers based on modulo 4 to analyze the 3x+1 problem, suggesting a new approach to proving the conjecture by examining number cycles.

Contribution

It introduces a classification scheme and cycle analysis for the 3x+1 problem, offering a new perspective for potential proof strategies.

Findings

Classification of numbers into four types by mod 4

Identification of cycles based on 3x+b1 problem

Proof of 3x+1 conjecture when certain number types are absent

Abstract

Under the 3x+1 problem, classified the number into four kind by mod 4. The four kind number can form a cycle base on 3x+b1 problem. Base on this cycle, if the number of kind number is zero the 3x+1 will be proofed.