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From: Gottfried Helms on 3 Aug 2010 03:54
Am 02.08.2010 22:45 schrieb Larry:
> Not surprisingly, I have found a fatal flaw in my argument. I
> suspected that this would be the case.
>
> It is Lemma 12 if anyone is interested. I had made the claim that:
>
> 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)
>
> Very sorry to have posted here when there was such an obvious
> mistake. I should have caught this myself before posting.
>
> Thanks to everyone who responded to my posts! I always appreciate
> honesty. :-)
>
> -Larry
Hi Larry -

good to see that.
I've taken a look into your text, and although there is a lot
of things I know from my own fiddlings, it was not easy for me
whaich of the 16 items was the crucial one, that step that
"no one before could solve"... I suspected it was around item 16

If you like you may look into my own treatize, where I -beginning
at the same path like you - arrived at a more general argument, which
too is not yet solved and either collatz implies this (or vice versa)
See
http://go.helms-net.de/math/collatz/aboutloop/collloopintro_main.htm
(this is html, but only poorly formatted, and one of my first
hobby-treatizes on numbers at all)

or

http://go.helms-net.de/math/collatz/Collatz061102.pdf

which is more compact, better formatted - I'm doing another edition of
that text, but this is only 50% rewritten (and I don't know whether I
find the time to really proceed... :( )

Regards -

Gottfried Helms

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