# The 3n+1 conjecture

\begin{conjecture} Let $f(n) = 3n+1$ if $n$ is odd and $\frac{n}{2}$ if $n$ is even. Let $f(1) = 1$. Assume we start with some number $n$ and repeatedly take the $f$ of the current number. Prove that no matter what the initial number is we eventually reach $1$. \end{conjecture}

This problem is also called Collatz conjecture, Ulam conjecture, or the Syracuse problem. For a more extensive discussion, visit the \Def[wikipedia article]{Collatz_conjecture} or [L].

## Bibliography

[L] Jeffrey C. Lagarias: \arxiv[The 3x+1 problem: An annotated bibliography (1963--2000)]{math/0309224}

* indicates original appearance(s) of problem.

### Bruckman proved 3x+1 problem

From PlanetMath's forums:

> Bruckman has published his proof of the conjecture in the International Journal of Mathematical Education in Science and Technology,

> Vol 39, Issue 3 April 2008.

--

Victor Porton - http://www.mathematics21.org

### In The 3x+1 Problem: An

In The 3x+1 Problem: An Annotated Bibliography, II (2001-), Lagarias explains why this proof is incomplete.

### Somebody's efforts

At http://occampress.com/ somebody publishes something about 3n+1 problem. Read him and check whether he is true.

Victor Porton - http://www.mathematics21.org

## Peter Schorer, again a possible proof

Just last month, July 2014, Schorer published another paper which uses similar methods as from his 2008 paper, claiming again to have proven the conjecture. This is early, but I am wanting to know what the general opinion of Schorer is in the world of serious mathematicians. All of my research has turned up mixed reviews and heated arguments.