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Old 2008-04-24, 19:58   #4
Brian-E
 
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"Brian"
Jul 2007
The Netherlands

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I'm pessimistic. My intuition says that the problem is no easier than the 3n+1 conjecture to which davar55 refers and therefore - unless someone can find a second cycle by searching - it will not be solvable with currently known techniques. Even if a second cycle is found and maybe others too, we still won't be able to prove that all numbers reduce to one of these cycles.
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