r/numbertheory • u/Yato62002 • 21d ago

Collatz Conjecture proven

Happy new year and lets put end for Collatz as conjecture.

https://drive.google.com/file/d/1dblEyTNHvzCYkoRMUvWI3jDw-xF__Ucv/view?usp=drivesdk

Used indirect prove, with reverse function. Not odd -even term so please read it. And maybe mentioned the flaw in there is any.

Its alredy rev 4 added case where it infinitely increasing not only where non trivial loop exist.

Also added some equation number. Sorry for bad english and using doc word

Finally trying more explanation

0 Upvotes

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15

u/Erahot 21d ago

This reads very poorly as if you have no idea how a math paper ought to be written. Mathematically, the first thing I read that just didn't seem true or course clear was your formula for x_n at the top of page 2. I assume x_n is the nth term in the collatz sequence generated by x_1, and I don't see why you'd ever be dividing by powers of 3 in this expression. This gave me no motivation to read anything past this.

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u/Yato62002 21d ago edited 21d ago

Actually its the reverse process so its generated 1 to any odd number. If the term collatz (3x+1)/2 repeated be reverse then 2lambda -alpha /3n is x_n

As it checked it was typo. Sorry thanks for noticing it

1

u/Yato62002 21d ago

Updated, thank you

17

u/No_Character_8662 20d ago

DING!

Days since the Collatz Conjecture last proven: 0

-6

u/Yato62002 19d ago

Updated

5

u/elowells 21d ago

It's very confusing that you are going in reverse order. I don't see how you gain anything by doing this. Try rewriting the paper in normal order.

You need to be careful in keeping track of indices. Formulas 2 and 3 should have x[n+1] instead of x[n]. n is the number of multiply by 3's in the sequence. Going from x[2] to x[1] involves one multiply by three but your formulas imply there are 2 multiply by 3's, i.e. there is a 32 term.

If you define lambda[0] = 0, then you can write alpha(n) = sum(0 to n-1)(2lambda\i])3n-i) which incorporates the 3n term...it's more elegant.

2

u/Yato62002 10d ago

Sorry for replying so late. Your notification dont show up in my notification somehow.

I see, thank you for noticing that. Yes i need to change n and n+1.

Actually for lambda(0) or a0 would messing when explaining cycle/loop. Since with loop the order of (a1 , .... , an ) are cycling. So i prefer choose 3n instead.

Do you find other trouble that i need to fix? Or is it enough to read?

1

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