Found an argument for no cycles in the Collatz Conjecture that uses only elementary mathematics

[Larry]

Hi Everyone,

I recently learned about the Collatz Conjecture some 6 months ago and
instantly became fascinated by it. Intuitively, it seemed like the a
problem just begging for progress.

In the past six months, I have often thought that I have made progress
(for usually no more than an hour or two) but then I discover some
very stupid mistake which removes the progress completely.

Most likely, this hasn't changed. The argument that I came up with is
a lot longer than I would have liked and it is complicated enough that
I am very sure I made some minor mistakes and typos. I've gone
through this proof now for about 24 hours and I have not found any
major mistakes (although I have already corrected a bunch of minor
mistakes).

Since I am tired and since I am very glad to quickly be told about the
mistakes, I have decided to post the link to the argument on this
group. I will also send it to the Sci.Math group.

I am a math amateur so I am not claiming to have solved the cycle part
of the Collatz Conjecture. I am presenting my argument in hopes of
receiving corrections on math terminology, identification of gaps in
the proof, questions about anything that is not clear, and
identification of any glaring errors.

Here is the link:
http://proposedproofs.blogspot.com/2010/07/collatz-conjecture-no-cycles.html


Thanks very much for your time.

-Larry

[Larry]

> Here is the link:http://proposedproofs.blogspot.com/2010/07/collatz-conjecture-no-cycl...

>
> Thanks very much for your time.
>
> -Larry

Hi Everyone,

I hope that you don't mind another post by me. I simplified the
argument to a one-pager that consists of 9 assumptions to make the
argument easier to follow:
http://proposedproofs.blogspot.com/2010/08/collatz-conjecture-no-cycle-one-page.html

Please let me know if you have any comments to make the presentation
easier. I would also be very interested if you have a counter-
argument for why one of my assumptions is not true or is not
sufficiently proven.

[Larry]

An update: I found a fatal error in my argument.

It is Lemma 12 in the longer post.

There, I made this claim:
3^(n-1) + 3^(n-2)*2^a_1 + 3^(n-3)*2^(a_1 + a_2) + ... + 3*2^(a_1 + ...
+ a_{n-2}) + 2^(a_1 + ... + a_{n-1}) =

(3 + 2^(a_1))(3 + 2^(a_2))*...*(3 + 2^(a_{n-1}) - (3)(3 +
2^(a_2))*...*(3 + 2&(a_{n-1}) - 3^(n-2)

I do not believe that this error can be corrected.

I suspected that I would find such an error. Sorry that I didn't find
it before submitting to this thread.

-Larry

[Ernst]

 Cool enough Larry!    I know this is dated.  Much as dated as the origin of this forum since abandoned.
 
The Questions are eternal!