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Method for proving the collatz conjecture, would this work?

  1. Aug 9, 2013 #1
    Would it be possible to prove the collatz conjecture indirectly by demonstrating rules that apply to 'Collatz-like' conjectures? (I call anything where you simply change the values in the 3n+1 part of the conjecture to other values, holding everything else the same a Collatz-like conjecture)

    For instance if you could demonstrate that

    A. all infinitely increasing sequences of a Collatz-like conjecture follow [insert rule].
    B. all sequences that loop in a Collatz-like conjecture either contain '1' as part of the loop, or else [insert condition].
    C. when set to 3n+1, A requires that there be no infinitely increasing sequences, and B requires that all loops contain '1'.

    Would this prove the conjecture true? (I cannot think of an A and B that are both true and lead to C, but if someone found it, would it prove the conjecture?)

    Conversely if you had A and B as above, but instead of C had
    D. When set to 3n+1, A requires that there be at least one infinitely increasing set
    or
    E. When set to 3n+1, B requires that there be at least one set that loops and does not contain '1'

    would you be able to disprove the conjecture?
     
  2. jcsd
  3. Aug 9, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    Sure. It would be a more powerful proof, with the Collatz conjecture as special case.
     
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