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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 10:53 PM
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On 09/03/2017 10:45 PM, David Bernier wrote:
> 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


The Supplementum of 1760 is also known as E272:

http://eulerarchive.maa.org/docs/originals/E272.pdf



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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