Home » Subject » Number Theory » Combinatorial N.T.
Importance: High ✭✭✭
Author(s): Collatz, Lothar
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)


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