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

Masoud Allame; Abdollah Hadi-Vencheh

doi:10.20944/preprints202305.0071.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 2 May 2023 / Approved: 2 May 2023 / Online: 2 May 2023 (08:10:49 CEST)

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.

Collatz Conjecture; 3x + 1 Conjecture; base-2 numeral system

Computer Science and Mathematics, Algebra and Number Theory

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

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