Fermat's Polygonal Number theorem vs FLT?
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From: ThinkTank on 7 May 2010 07:09 See my response to Pubkeybreaker.
From: A on 7 May 2010 11:40 On May 7, 9:34 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > On May 7, 8:50 am, ThinkTank <ebigl...(a)gmail.com> wrote: > > > > On May 4, 5:16 am, ThinkTank <ebigl...(a)gmail.com> > > > wrote: > > I'm not sure how you can say they are a completely > > different issue. There are many similarities between the > > two problems. Most notably, both are statements about > > sums of n-symmetric shapes, > > If you don't know the difference between a curve and a surface, I give > up. > You are so totally clueless about mathematics that you > are not even aware of the DEPTH of your ignorance. > > However, in this particular instance, I will tell you the difference. > > Varieties over SURFACES have many more 'degrees of freedom' than > varieties over curves. A^4 = B^4 + C^4 + D^4 *HAS* solutions. > Infinitely many. > > They are different problems. They are different problems, but surfaces are indeed used to study curves--for example, Doug Ulmer's proof that elliptic curves over function fields can have arbitrarily large rank, this uses an elliptic surface--the total space of some family of elliptic curves parameterized by some curve--in an essential way. I mean, the OP certainly appears to be misguided and misinformed at best; but I think the reason you gave isn't one of the best reasons to suspect that the OP has a poor understanding of number theory.
From: ThinkTank on 7 May 2010 07:54 > On May 7, 7:20 am, "Achava Nakhash, the Loving Snake" > <ach...(a)hotmail.com> wrote: > > On May 6, 1:00 am, ThinkTank <ebigl...(a)gmail.com> > wrote: > > > > > > yeah, that's the spirit. the problem is, > > > > in developing a model of n-dimensional figurate > > > > numbers, > > > It says nothing about one polygonal number being > representable as a > > sum of 2 polyngonal numbers. None of 3, 4, 5, 6, > etc. are equal to 2, > > and the representation is of ALL INTEGERS and not > of another figurate > > number. Again, the connection with Fermat's Last > Theorem eludes me is > > almost surely completely bogus. > > Note also that the Fermat equation is an algebraic > plane CURVE, It was originally stated, by Fermat, as a Diophantine equation, not as an algebraic plane curve. As I have basically already pointed out, Fermat's little theorem: x^p == x (mod p) could be regarded as a statement about the symmetry of the figurate number x^p. Furthermore, consider that the rth coefficient of binomial expansion of x^p are is the is the pth regular r-polytopic number. There is clearly a DEEP connection between Fermat's Polygonal Number Theorem and Fermat's Last Theorem, and I am baffled by the fact that you, Gerry, and Tonio can't see this. > whereas > in talking about polygonal numbers, the OP is now > talking about > varieties > on SURFACES --> A totally different problem. > I never claimed it wasn't a different problem, but it is CLEARLY NOT totally different. There are DEEP connections between these two problems. > And the OP is too ignorant to realize it. No Message was edited by: Ehren Biglari
From: Mike Terry on 7 May 2010 12:21 "ThinkTank" <ebiglari(a)gmail.com> wrote in message news:647707652.80373.1273130368529.JavaMail.root(a)gallium.mathforum.org... > > In article > > <1853636941.69435.1272978833774.JavaMail.root(a)gallium. > > mathforum.org>, > > ThinkTank <ebiglari(a)gmail.com> wrote: > > > > > > On May 4, 10:16� pm, ThinkTank > > <ebigl...(a)gmail.com> > > > > wrote: > > > > > If Fermat's original proof of the Fermat > > Polygonal > > > > Number > > > > > Theorem has not yet been found, why are > > > > mathematicians so > > > > > quick to assume that Fermat did not have an > > > > extension to > > > > > that proof which may have led to the proof of > > > > Fermat's Last > > > > > Theorem? It seems to me the key to > > understanding > > > > FLT lies > > > > > in a simple inductive proof for Fermat's > > Polygonal > > > > Number > > > > > theorem. > > > > > > > > What nonsense. > > > > > > Yes, what nonsense? I barely said a thing. > > > > You said "It seems to me the key to understanding FLT > > > > lies in a simple induvtive proof for Fermat's > > Polygonal > > Number Theorem." I'll stand by my response. > > > > And I stand by my response to your response. Would you > like to do this again? To avoid an infinite loop, let me sumarise: It is accepted that ThinkTank hardly said anything, but what he/she did say was nonsense. :) HTH, Mike.
From: Jesse F. Hughes on 7 May 2010 12:22
ThinkTank <ebiglari(a)gmail.com> writes: >> On May 7, 6:26 am, ThinkTank <ebigl...(a)gmail.com> >> wrote: >> > > In article >> > > >> <677236230.80457.1273132878888.JavaMail.r...(a)gallium.m >> > > athforum.org>, >> > > ThinkTank <ebigl...(a)gmail.com> wrote: >> > >> > > > ""...an isomorphism between the integers and >> the >> > > reals..." >> > >> > > Thanks for removing any trace of doubt >> > > about your mathematical knowledge. >> > >> > And you, Gerry, have proven that you do not READ >> the >> > posts. Besides that fact, I was speaking informally >> to >> > save time. Perhaps you have all the time in the >> world to >> > waste, but I do not. >> >> Gerry discerned the content of your posts quite >> clearly. > > No, he did not, and apparently you don't READ either. He > did not quote me correctly. > Here's the quote in context. However, I have developed a completely different proof, which does not rely on either of these, but rather on Galois fields, and an isomorphism between the integers and the reals. >> I stand with him. You are a crank, and you are >> mathematically >> clueless. Your claim of an > > You have no evidence to support that claim. Your quote > is not even correct. You, Gerry and Tonio are grasping > at straws here. I have made absolutely NO mathematical > mistakes in ANY of my posts so far. NONE. Not ONE. > Until you, Gerry or Tonio can point out a contradiction > or mistake in my statements, you have no case. It seems to me that you claimed to have a proof that "relies on" an isomorphism between the integers and the reals. This fact would be interesting only if there is, in fact, an isomorphism between the integers and the reals, so it was perfectly natural to read you as saying there is such an isomorphism. Is this not what you meant? Do you think there is an isomorphism between N and R or not? -- Jesse F. Hughes "How can I miss you when you won't go away?" -- Dan Hicks and his Hot Licks |