Method for proving the collatz conjecture, would this work?

1. Aug 9, 2013

firlz

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?)

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. Aug 9, 2013

Staff: Mentor

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