# Collatz Conjecture Proof? **URL:** \ **Category:** Factual Questions\ **Created:** [October 20, 2017, 7:41am UTC](https://boards.straightdope.com/t/collatz-conjecture-proof/799356 "2017-10-20T07:41:53Z")\ **Posts on this page:** 3\ **Page:** 2
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [July 20, 2019, 7:51pm UTC](https://boards.straightdope.com/t/collatz-conjecture-proof/799356/21 "2019-07-20T19:51:29Z")
[Did Paul Erdős leave $500 sitting somewhere for the person](https://blogs.ams.org/mathgradblog/2013/08/01/collatz-conjecture/) who shows that [mathematics IS ready for such problems](https://store.xkcd.com/products/collatz-conjecture)? ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [July 21, 2019, 2:40am UTC](https://boards.straightdope.com/t/collatz-conjecture-proof/799356/22 "2019-07-21T02:40:29Z")
> [@Enola\_Straight](#): > > As I understand it, The Collatz conjecture is to find out whether or not, starting with an initial integer, you indeed end up with the 4-2-1 loop; maybe you end up with another loop, or you spiral out to infinity. > > As Sage Rat stated there is a series of permutations of two functions: > > a=x/2 > b=3x+1 > > What, if anything, new can we learn if, starting with 1, we work _backward_ by reversing the functions? > > Starting with 1, sprout two new branches: > > a’=2x > b’=3/x-1 Reversing from 1 would simply give you formulas that reach 1 (if the number 1 itself is, in fact, part of your math). That wouldn’t tell you anything except which numbers go to 1. Granted, it might produce gaps and, if the gaps stayed open long enough that might provide a number worth analyzing. But I don’t that this is a particular efficient means of search. If you’re simply looking for pathways, rather than numbers, then whether you go through the path forwards or backwards isn’t particularly meaningful. A reversed formula is equivalent to a forwards formula. All that we really care about is whether there’s a path that loops and doesn’t include the number 1. Where that occurs is inconsequential so anything which would root it to the number 1, or any point in the number line, should be less efficient than any method which simply doesn’t care. Of course, all search mechanisms are potentially less efficient than finding some math that proves the case one way or the other. If someone can demonstrate that: 3^h / 2^g x + (3^h - 1) / 2 Will never produce a whole number, except the number 1, for whole numbers of h and g \>= 0 and x \>= 1, then you can conclusively state that there are no loops in Collatz. In theory, it might still diverge, but there are no loops. That might be a simple thing for a mathematician. It’s a thing that I’m intending to investigate as well since it’s a very efficient means of proving something. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 21, 2019, 12:37pm UTC](https://boards.straightdope.com/t/collatz-conjecture-proof/799356/23 "2019-07-21T12:37:29Z")
> [@](#): > > Quoth **Enola Straight** : > > Btw, I figure, since we’re reversing, you don’t use one function OR the other depending on whether or not that particular integer is even or odd, you branch BOTH functions to generate BOTH even and odd You can always take the 2n branch, but you can’t always take the (n-1)/3 branch. If you’re at 5, for instance, (n-1)/3 would give you 4/3, which isn’t an integer. And even if you’re at 7, (n-1)/3 would give you 2, an integer, but you still can’t take that branch, because 2 is even: Under the forward Collatz rules, 2 goes to 1, not 7. [Previous page](https://boards.straightdope.com/t/collatz-conjecture-proof/799356.md?page=1)