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Topic: Nineteen months.
Replies: 42   Last Post: Mar 4, 2007 3:51 PM

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 Nico Benschop Posts: 17 Registered: 9/7/06
Re: Nineteen months / Goldbach-FLTsemigroups
Posted: Feb 28, 2007 9:44 AM

"Hisanobu Shinya" <eprinthshinya@yahoo.com> schreef in bericht
news:17979822.1172596033376.JavaMail.jakarta@nitrogen.mathforum.org...
> [ . . . ]
> I saw the term semigroup, which I do not know much about.
> I only know undergraduate modern algebra.

in essence the associative algebra of function composition) and
their practical applications, have a look at my (online) book:
. . . "Associative Digital Network Theory"
http://home.iae.nl/users/benschop/preface.htm
It has three parts:
- - state machines (associative algebra),
- - arithmetic (associative and commutative),
- - logic (associative and commutative and idempotent),
divided up in a total of 11 chapters and 3 appendices.
(the latter including the proofs of FLT and Goldbach
by the residue-and-carry method).
For intro to the relation of semigroups and FLT :
see http://home.iae.nl/users/benschop/sgrp-flt.htm
and http://home.iae.nl/users/benschop/carry.htm

>> Which I did: my 'residue-and-carry' method also applies to Goldbach,
>> but with another modulus (than p^k for FLT), namely the product of
>> the first k primes, followed by careful extension with one carry of
>> weight p_{k+1} and induction on k. Saying that any FLT proof after
>> Wiles' (of 1995) is useless shows a lack of understanding of how
>> mathematics develops! Frankly, to use the Tanyama-Shimura proof
>> (of 150+20 pgs) as a method to prove FLT is a bit 'over-the-top',
>> don't you think? It is like going to the next room via the Northpole. - -
>> NB.

>
> I am sorry. I do not understand even the statement of Taniyama-Shimura.