Number Theory


Proof of the 3n+1 Problem for N ≥ 1

Authors: Steffen Bode

I establish the existence of a unique binary pattern inherent to the 3n+1 step, and then use this binary pattern to prove the 3n+1 problem for all positive integers.

Comments: 6 Pages.

Download: PDF

Submission history

[v1] 10 May 2010

Unique-IP document downloads: 761 times

Articles available on are pre-prints that may not yet have been verified by peer-review and should therefore be treated as preliminary and speculative. Nothing stated should be treated as sound unless confirmed and endorsed by a concensus of independent qualified experts. In particular anything that appears to include financial or legal information or proposed medical treatments should not be taken as such. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus