Difference between revisions of "Collatz Problem"
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| − | Define the following [[function]] on <math>\mathbb{N}</math>: <math>f(n)=\begin{cases} 3n+1 & 2\nmid n, \\ \frac{n}{2} & 2\mid n.\end{cases}</math> The Collatz conjecture | + | Define the following [[function]] on <math>\mathbb{N}</math>: <math>f(n)=\begin{cases} 3n+1 & 2\nmid n, \\ \frac{n}{2} & 2\mid n.\end{cases}</math> The Collatz conjecture says that, for any [[positive integer]] <math>n</math>, the sequence <math>\{n,f(n),f(f(n)),f(f(f(n))),\ldots\}</math> contains 1. This conjecture is still open. Some people have described it as the easiest unsolved problem in mathematics. |
Revision as of 12:53, 18 July 2006
Define the following function on 
: 
The Collatz conjecture says that, for any positive integer 
, the sequence 
contains 1. This conjecture is still open. Some people have described it as the easiest unsolved problem in mathematics.
