Preprint

Article

Altmetrics

Downloads

1588

Views

3418

Comments

1

A peer-reviewed article of this preprint also exists.

Bülent Sukuşu

Bülent Sukuşu

This version is not peer-reviewed

Collatz conjecture (or 3n+1 problem) has been explored for about 85 years. In this article, we prove the Collatz conjecture. We will show that this conjecture is valid for all positive integers by performing the Collatz inverse operation on the numbers that comply with the rules of the Collatz conjecture. Finally, it will be proved that there are no positive integers that do not comply with this conjecture.

Keywords:

Subject: Computer Science and Mathematics - Algebra and Number Theory

Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

Submitted:

14 November 2022

Posted:

15 November 2022

Read the latest preprint version here

Alerts

A peer-reviewed article of this preprint also exists.

Bülent Sukuşu

Bülent Sukuşu

This version is not peer-reviewed

Submitted:

14 November 2022

Posted:

15 November 2022

Read the latest preprint version here

Alerts

Collatz conjecture (or 3n+1 problem) has been explored for about 85 years. In this article, we prove the Collatz conjecture. We will show that this conjecture is valid for all positive integers by performing the Collatz inverse operation on the numbers that comply with the rules of the Collatz conjecture. Finally, it will be proved that there are no positive integers that do not comply with this conjecture.

Keywords:

Subject: Computer Science and Mathematics - Algebra and Number Theory

Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?

Masoud Allame

et al.

,

2023

Analyzing Collatz Conjecture Using the Mathematical Complete Induction Method

Mercedes Orús-Lacort

et al.

,

2022

© 2024 MDPI (Basel, Switzerland) unless otherwise stated