Version 1
: Received: 2 May 2023 / Approved: 2 May 2023 / Online: 2 May 2023 (08:10:49 CEST)
How to cite:
Allame, M.; Hadi-Vencheh, A. Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints2023, 2023050071. https://doi.org/10.20944/preprints202305.0071.v1
Allame, M.; Hadi-Vencheh, A. Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints 2023, 2023050071. https://doi.org/10.20944/preprints202305.0071.v1
Allame, M.; Hadi-Vencheh, A. Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints2023, 2023050071. https://doi.org/10.20944/preprints202305.0071.v1
APA Style
Allame, M., & Hadi-Vencheh, A. (2023). Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints. https://doi.org/10.20944/preprints202305.0071.v1
Chicago/Turabian Style
Allame, M. and Abdollah Hadi-Vencheh. 2023 "Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?" Preprints. https://doi.org/10.20944/preprints202305.0071.v1
Abstract
This study focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The Collatz conjecture or 3x + 1 Problem is perhaps today's most enigmatic unsolved mathematical problem. It is named after Lothar Collatz, who rst proposed it in 1937. It may be stated as as follow: Take any positive integer n. If n is even then divide it by 2, else do \triple plus one" and get 3n + 1. The conjecture is that this process will eventually reach the number 1, regardless of which positive integer is chosen initially. In this paper, we present a simple proof for the Collatz conjecture.
Keywords
Collatz Conjecture; 3x + 1 Conjecture; base-2 numeral system
Subject
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.