The Famous Collatz Sequence (or Conjecture)

This sequence made a MATHEMATICIAN say that MATH is NOT READY for these types of problems.


First, you choose a number. The rules of the sequence are:

If the number is odd, multiply it by 3 and then add 1.

If the number is even, divide it by 2

Repeat.

So for 3, the string would be : 3 - 10 - 5 - 16 - 8 - 4 - 2 - 1.

And the question is: Do all numbers end in 1?

They have proven this to very big numbers. But not ALL the numbers. Not when the numbers tend to infinity and beyond (pun intended).

The problem with this is that when we add 1, it has an IMMENSE effect on the factors of a number unlike when we multiply by 3 or divide by 2. We need to discover this-this ... "Theorem of this change in factors ". \[\] \[\] Only if we can. \[\] \[\] This is what made a mathematician say that Math is not ready for such problems. The notorious plus sign was present in Fermat's Last Theorem and so is it over here. It took 7 years and 200 pages for Fermat's Last Theorem's proof. (almost disproven by \(6^3+8^3=9^3-1)\) \[\] \[\] Maybe this takes more. \[\] \[\] Maybe it is going to stay unsolved. \[\] \[\] Maybe we are not going to see the proof in our lifetimes. \[\] \[\] \[\] MAYBE is the word. Never lose hope. Stay hydrated with hope. Saturated and when there is a will there is a way. \[\] \[\] \[\] \[\] Maybe we will solve it \[\] \[\] \[\] \[\]


P.S. Sorry for being dramatic. (CORRECTION- Overdramatic)

Note by Mohmmad Farhan
1 month ago

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When Erdos says that this problem is hard, you may want to take his word; he offered such a small sum of money for its solution because he knew damn well that the problem may never be solved. While it may never be proved in the foreseeable future, it may also never be disproved; in any case, you will find that not many people care much about this problem.

On a happier note, I have an interesting question for you: What happens if we modified the \(3\) in the sequence formulation to some other odd number? Obviously changing it to an even number would not work out well, but if we replaced the \(3\) with a \(5\) it's not hard to see (computationally or analytically) that picking a small starting point could and would blow this sequence up to a point that we may never reach \(1\) ever. Is the choice of \(3\) unique? Have a think about these questions.

Gennady Notowidigdo - 4 weeks, 1 day ago

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