Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

3x + 1 Problem: Iterative Operations Neither Cause Loops nor Diverge to Infinity

Version 1 : Received: 20 May 2021 / Approved: 21 May 2021 / Online: 21 May 2021 (07:52:14 CEST)

How to cite: Jiang, L. 3x + 1 Problem: Iterative Operations Neither Cause Loops nor Diverge to Infinity. Preprints 2021, 2021050499 (doi: 10.20944/preprints202105.0499.v1). Jiang, L. 3x + 1 Problem: Iterative Operations Neither Cause Loops nor Diverge to Infinity. Preprints 2021, 2021050499 (doi: 10.20944/preprints202105.0499.v1).

Abstract

The 3x+1 problem is a problem of continuous iteration for integers. According to the basic theorem of arithmetic and the way of iteration, we derive a general formula for continuous iteration for odd integers. Through this formula, we can construct a loop iteration equation and obtain the result of the equation: the equation has only one positive integer solution. In addition, this general formula can be converted into a linear indeterminate equation. The process of solving this equation shows that the relationship between the iteration result and the odd number being iterated is linear. Extending this result to all positive even numbers, we get the answer to the 3x + 1 question.

Subject Areas

3x + 1 problem; Collatz conjecture; Syracuse problem; iteration

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.