Daedalus
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I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.
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I'm going to state this before we go on, I don't think the Collatz conjecture will be solvable with simple fiddling of mathematical axioms, though it could happen. Many Mathematicians have attempted to solve this problem without any progress, really. Although your equation might make the problem easily understood, I don't think it will solve it. This problem might require a solution that works outside the given axioms and analyzes the axioms from a more complex standpoint. Fermat...
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