Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers

EasyChair Preprint 13029

Abstract

This study delves into a unique binary pattern found within the wellknown
3n+1 problem, or Collatz conjecture. Through careful analysis of
the steps in the 3n+1 sequence, we have discovered a special binary representation
that captures the behavior of all positive integers undergoing
this transformation. With this new understanding, we have provided a
solid proof confirming the validity of the 3n+1 problem for all positive
integers. Our method goes beyond the need for extensive computational
confirmation, providing a simple and elegant resolution to a long-standing
mathematical mystery.

Keyphrases: Binary Pattern, Collatz Conjecture, positive integers

@booklet{EasyChair:13029,
  author    = {Budee U Zaman},
  title     = {Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers},
  howpublished = {EasyChair Preprint 13029},
  year      = {EasyChair, 2024}}