|
Download PDFOpen PDF in browserRevealing a Binary Pattern Validates 3n+1 Problem for All Positive IntegersEasyChair Preprint 130296 pages•Date: April 16, 2024AbstractThis 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 Download PDFOpen PDF in browser |
|
|