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Topic: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT, a
huge gap error in both offerings

Replies: 44   Last Post: Sep 6, 2017 5:18 PM

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David Bernier

Posts: 3,884
Registered: 12/13/04
Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings

Posted: Sep 3, 2017 10:45 PM
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On 09/03/2017 03:51 PM, David Bernier wrote:
> On 09/03/2017 07:12 AM, David Bernier wrote:
>> On 09/02/2017 04:01 PM, Nobody wrote:
>>> On 9/2/2017 6:12 PM, Archimedes Plutonium wrote:
>>>> First the Euler big huge mistake in FLT
>>> ...
>>>> Now it is horribly amazing that from 1770 to 2016, no-one in the math
>>>> community had enough logical brains to realize the gaping hole in
>>>> Euler's alleged proof of case exponent 3.
>>>>
>>>> Laughable, how crippled of logic are most math professors. Laughable
>>>> how they would accept the above proof of exponent 3.
>>>>
>>>> Why so harsh on Euler? What was Euler's mistake? And am I justified
>>>> in being so harsh?
>>>>
>>>> Yes, I am justified in being so harsh, because what Euler missed is
>>>> that his so called proof covers only the fact of when A, B, C are two
>>>> odds with one even. Euler completely loses the fact that a solution
>>>> in exponent 3 can occur when A, B, C are all three even numbers.

>>>
>>> The case of A, B, C being all even is not interesting. If A, B, C are
>>> all even, the equation can be rewritten with A=2D, B=2E, C=2F with D,
>>> E, F all integral because A, B, C are all even.
>>> We now have an equation (2D)^3+(2E)^3=(2F)^3.
>>> Or, 8D^3+8E^3=8F^3.
>>> Factor out 8 and we now have a new equation of the form D^3+E^3=F^3. The
>>> exact same problem. However, there is a difference. Either D, E, F are
>>> not all even or they are. If they aren't, the all even problem just
>>> reduces to a not all even problem. If they are all even, simply
>>> repeat the divide by 8 step, repeatedly if necessary, until one or
>>> more are not even.
>>>
>>> Just like with Pythagorean triangles. The first is the 3,4,5
>>> triangle. There is also a 6,8,10 triangle, but all it is is the 3,4,5
>>> triangle scaled up.

>>
>> Typical of AP: little math intuition, overconfidence, and hubris.
>>
>> Euler :
>>
>> (a) Proved 2^32 + 1  composite, disproving Fermat on Fermat primes.
>>
>> (b) Summed the series: 1/1^2 + 1/2^2 + 1/3^2 + ... = pi^2/6 .
>>
>> (c) Solved the Konigsberg Bridge Problem.

>
> After looking things up, I'd say the 1770 proof/argument in Euler's
> Algebra had
> a gap, a true-to-form small gap, and it was noticed by a few.
> As things standed, infinite descent was in question, unless the gap
> was resolved.
>
>
> This was discussed in 2000 in sci.math :
>
> "[HM] Fermat's Last Theorem (was: al-handasah)"
> by Franz Lemmermeyer, at:
>
> < http://mathforum.org/kb/message.jspa?messageID=1180657 > .
>
>
>
> Lemmermeyer wrote:
>
> "BTW, in
> Supplementum quorundam theorematum arithmeticorum
> quae in nonnullis demonstrationibus supponuntur,
> Novi. Comm. Acad. Sci. Petrop. 8 (1760/61), 1763, 105--128;
> Opera Omnia I - 2, 556--575
> Euler closes the gap in a proof of FLT for n = 3 that has apparently
> never appeared in print (is this correct? My Latin [...] "
>
>
> Emili Bifet wrote:
>
> "Dear All,
> This "Supplementum ..." is available on-line at BnF:
> http://gallica.bnf.fr/scripts/get_page.exe?F=PDF&O=006952&E=596&N=20&CD=1
> (20 pages in Latin, ~1 MB) "
>
>
>
> Paulo Ribenboim also mentions Euler's 1760 "Supplementum quorandum...."
> in the References for Lecture III, "B.K." Before Kummer,
> at:
>
> "13 Lectures on Fermat's Last Theorem" ( Ribenboim ):
>
> < https://books.google.ca/books?id=c6TTBwAAQBAJ > .
>


I was trying to figure out how much Euler proved, and how much or
what he assumed without proof, if anything, in his
1760 communication to the St. Petersburg Academy.

It's in Latin, which I can't read, so I'm not sure.

The Latin expression:

De numeris formae aa + 3bb

appears at the top of this work as it appears in
reprinted in "Euler's works" under vatious editions.

David Bernier


Date Subject Author
9/2/17
Read Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT, a
huge gap error in both offerings
plutonium.archimedes@gmail.com
9/2/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
Pi the 13th deity
9/2/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
David Bernier
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
David Bernier
9/3/17
Read is Old Math trying to rewrite history here, to suit themselves Re:
Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT, a huge gap
error in both offerings
plutonium.archimedes@gmail.com
9/3/17
Read all the cases of FLT, Fermat, Euler, Dirichlet & Legendre were flawed
Re: is Old Math trying to rewrite history here, to suit themselves
plutonium.archimedes@gmail.com
9/3/17
Read Re: all the cases of FLT, Fermat, Euler, Dirichlet & Legendre were
flawed Re: is Old Math trying to rewrite history here, to suit themselves
bursejan@gmail.com
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
David Bernier
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
David Bernier
9/3/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
Me
9/4/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
bernierdavid529@gmail.com
9/4/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
bernierdavid529@gmail.com
9/5/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
bursejan@gmail.com
9/3/17
Read when was the first Generalized FLT? 1844? Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read FLT is still kicking Re: Comparing the Wiles flaw of FLT with the
Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read nearing a denouement Re: FLT is still kicking Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read finally FLT has stopped kicking Re: Comparing the Wiles flaw of FLT
with the Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read finally FLT has stopped kicking Re: Comparing the Wiles flaw of FLT
with the Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read Re: finally FLT has stopped kicking Re: Comparing the Wiles flaw of
FLT with the Euler flaw of exp3 FLT, a huge gap error in both offerings
bursejan@gmail.com
9/5/17
Read Re: finally FLT has stopped kicking Re: Comparing the Wiles flaw of
FLT with the Euler flaw of exp3 FLT, a huge gap error in both offerings
bursejan@gmail.com
9/5/17
Read Re: FLT is still kicking Re: Comparing the Wiles flaw of FLT with the
Euler flaw of exp3 FLT, a huge gap error in both offerings
Richard Tobin
9/5/17
Read Re: FLT is still kicking Re: Comparing the Wiles flaw of FLT with the
Euler flaw of exp3 FLT, a huge gap error in both offerings
plutonium.archimedes@gmail.com
9/5/17
Read Array Proofs of Generalized FLT, and of FLT
plutonium.archimedes@gmail.com
9/5/17
Read Re: Array Proofs of Generalized FLT, and of FLT
bursejan@gmail.com
9/5/17
Read Re: Array Proofs of Generalized FLT, and of FLT
bursejan@gmail.com
9/5/17
Read Re: Array Proofs of Generalized FLT, and of FLT
bursejan@gmail.com
9/5/17
Read Re: Array Proofs of Generalized FLT, and of FLT
bursejan@gmail.com
9/5/17
Read Re: Array Proofs of Generalized FLT, and of FLT
bursejan@gmail.com
9/6/17
Read Re: FLT is still kicking Re: Comparing the Wiles flaw of FLT with the
Euler flaw of exp3 FLT, a huge gap error in both offerings
Richard Tobin
9/6/17
Read Pythagorean Lemma & Generalized FLT lemma Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read Re: Pythagorean Lemma & Generalized FLT lemma Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
bursejan@gmail.com
9/5/17
Read Tobin ahead of Wiles in understanding FLT Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/5/17
Read Re: Tobin ahead of Wiles in understanding FLT Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read Re: Tobin ahead of Wiles in understanding FLT Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read Re: Tobin ahead of Wiles in understanding FLT Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read FLT, still kicking Re: Comparing the Wiles flaw of FLT with the Euler
flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read maybe FLT cannot come from Generalized FLT Re: Comparing the Wiles
flaw of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read looking good, looking good Re: Comparing the Wiles flaw of FLT with
the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read looking good, looking good Re: Comparing the Wiles flaw of FLT with
the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/6/17
Read Re: looking good, looking good Re: Comparing the Wiles flaw of FLT
with the Euler flaw of exp3 FLT
bursejan@gmail.com
9/6/17
Read Alright, the Lemma I needed to prove FLT Re: Comparing the Wiles flaw
of FLT with the Euler flaw of exp3 FLT
plutonium.archimedes@gmail.com
9/2/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
bursejan@gmail.com
9/2/17
Read Re: Comparing the Wiles flaw of FLT with the Euler flaw of exp3 FLT,
a huge gap error in both offerings
bursejan@gmail.com

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