The 3n+1 conjecture

Importance: High ✭✭✭

Author(s):

Subject:	Number Theory
	» Combinatorial Number Theory

Keywords:

integer sequence

Recomm. for undergrads: no

Prize: $500 by Paul Erdős

Posted	by:	dododododo
	on:	July 13th, 2007

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 $1$ .

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

Bibliography

[L] Jeffrey C. Lagarias: The 3x+1 problem: An annotated bibliography (1963--2000)

* indicates original appearance(s) of problem.

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Peter Schorer, again a possible proof

On July 11th, 2014 Anonymous says:

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.

Bruckman proved 3x+1 problem

On April 9th, 2008 porton says:

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