Version 1
: Received: 15 April 2024 / Approved: 15 April 2024 / Online: 15 April 2024 (10:55:15 CEST)
How to cite:
U Zaman, B. Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers. Preprints2024, 2024040943. https://doi.org/10.20944/preprints202404.0943.v1
U Zaman, B. Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers. Preprints 2024, 2024040943. https://doi.org/10.20944/preprints202404.0943.v1
U Zaman, B. Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers. Preprints2024, 2024040943. https://doi.org/10.20944/preprints202404.0943.v1
APA Style
U Zaman, B. (2024). Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers. Preprints. https://doi.org/10.20944/preprints202404.0943.v1
Chicago/Turabian Style
U Zaman, B. 2024 "Revealing a Binary Pattern Validates 3n+1 Problem for All Positive Integers" Preprints. https://doi.org/10.20944/preprints202404.0943.v1
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.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
