Solution to Collatz Conjecture

Abhijit Manohar^1,

¹Kolhapur, Maharashtra, India

Cite this paper

Abhijit Manohar. Solution to Collatz Conjecture. American Journal of Applied Mathematics and Statistics. 2021; 9(3):107-110. doi: 10.12691/AJAMS-9-3-5

Abstract

Collatz Conjecture, one of the unsolved problems in mathematics is that for any positive integer, the positive integer is multiplied by 3 and 1 is added if odd, divided by 2 if even. This process is repeated, and the sequence of numbers finally reaches 1. Collatz Conjecture is notoriously escaped all attempted proofs. This paper presents a solution to Collatz Conjecture with a statistical and logical/ mathematical proof. The article demonstrates why Collatz function cannot enter an iterative infinite loop and the function will reach 1 for all positive integers.

Keywords

Collatz Conjecture, Diverging and Converging functions, Collatz Function, Alternating Functions, Collatz Product, Weighted Even Decreasing Function, Iterative Loop

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Kossak, Roman. Mathematical Logic: On Numbers, Sets, Structures and Symmetry. Springer Graduate Texts in Philosophy, Volume 3, Springer International Publishing AG, part of springer nature 2018, ISBN 978-3-319-97298-5.
[2]	Honner, Patrick. (2020). The simple Math problem we still cannot solve. Quantamagazine. The Simple Math Problem We Still Can’t Solve | Quanta Magazine.