Version 1
: Received: 31 July 2024 / Approved: 1 August 2024 / Online: 1 August 2024 (12:33:24 CEST)
How to cite:
Shiraishi, H.; Shiraishi, H. Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder. Preprints2024, 2024080021. https://doi.org/10.20944/preprints202408.0021.v1
Shiraishi, H.; Shiraishi, H. Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder. Preprints 2024, 2024080021. https://doi.org/10.20944/preprints202408.0021.v1
Shiraishi, H.; Shiraishi, H. Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder. Preprints2024, 2024080021. https://doi.org/10.20944/preprints202408.0021.v1
APA Style
Shiraishi, H., & Shiraishi, H. (2024). <strong></strong>Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder. Preprints. https://doi.org/10.20944/preprints202408.0021.v1
Chicago/Turabian Style
Shiraishi, H. and Hajime Shiraishi. 2024 "<strong></strong>Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder" Preprints. https://doi.org/10.20944/preprints202408.0021.v1
Abstract
In solving the Collatz conjecture, it turns out that if we let all integers k be 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5, then we can solve the Collatz conjecture periodically. The Collatz conjecture states that for any positive integer P (initial value), if n is even, divide n by 2; if n is odd, repeat the rule of multiplying n by 3 and adding 1, which always converges to 1. One open problem has been proved by this paper. The authors hope to contribute to the mathematical community by presenting simple proofs of conjectures in the history of mathematics such as the Collatz conjecture.
Keywords
Collatz conjecture; 6n; regularity
Subject
Computer Science and Mathematics, Mathematics
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.
