Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum Fermat paper in WSEAS journal July 2004

Hi, I have a new paper in WSEAS Transactions on Mathematics, July 2004, entitled: "Fermat's Last Theorem: Proof Based on Generalized Pythagorean Diagram." The paper will be posted soon on arXiv.org I have a newer unpublished paper also on the Goldbach Conjecture, being typeset and will be submitted to a journal within a week or so. I have 3 Goldbach proofs: 2 of the Goldbach Conjecture, and 1 of the Odd Goldbach Conjecture. However, the two short papers need careful checking. I may submit them to a journal if I can verify them. The longer Goldbach proof paper I believe is very solid but will recheck this over the next few weeks.

In regard to my published Fermat paper, there have been no critiques to speak of since its release in late August 2004. (None of the critiques have come from anyone who has read the full paper.) WSEAS published after independent review by 3 referees.

If you would like to see a summary of my Fermat paper now, please look at mathforge.net and search for Fermat paper by Jay Dillon. (Look in their news archives.) This is a simple proof method:

A Pythagorean-styled area diagram is used to represent any FLT-form equation, indeed it can be used to represent any equation of the form A + B = C, just illustrate "A", "B", "C" as arbitrarily drawn square areas in 2D.

This leads to a method for full generalization of the illustration to apply to all possible true FLT-form equations.

Try it. Look for the full paper in WSEAS Transactions on Mathematics or soon on arXiv.org --assuming arXiv.org will allow me to post there. (WSEAS has now granted me permission to post the full paper online.)

Please note that this posting on Science a GoGo does not embody my entire proof method. Please read the full paper and avoid attacking my method after considering only the first few steps.

thank you

Jay, and what exactly is the reason for the self-advertising on Agogo? You have one published paper, fine, you have three more drafts in works, fine again.And so what?Why exactly do you need popular approval?

Oh, and if you need critique/oppinions about your work, I suggest you first upload your drafts on arxiv, wait for the reactions, and after you got some feedback (if any), make the necesary corrections/additions and publish it.

Yes Jay; Fermat's Last has been the "grit" around which many a mathematical "pearl" has been grown over the centuries, Euler being one of the "clams"; so you join an elite club. A^n+B^n not=to C^n where n>2, whilst simple to state, implies...what? 3^2+4^2=5^2 is the simplest area statement of the pythagorean series. 3^3+4^3+5^3=6^3 being the lowest of the volume series<next is 8^3+6^3+1^3=9^3>. Norrie<circa 1910>found 30^4+120^4+272^4+315^4=353^4 for the fourth power series, tough to do as 4th powers only end in 0,1,5 or 6 plus rapid divergence. Fifth powers diverge even more rapidly but do end in 1,2,3....8,9 mods. Do you know of a solution to A^5+B^5+C^5+D^5+E^5=F^5?<diophantine series> Having wrestled with Fermat years ago I came to realize the "secret" is in the + sign of A^n + B^n = C^n : the # of elements added on the left side must = the vector-dimensional elements on the right side : 1+1=2<area> 1+1+1=3<volume> 1+1+1+1=4<tube> So, rotate + symbol 45 deg to x and - symbol 45 deg to /...This then gave me 2, then 4, multiplication/division laws : 1:Multiplication is repetitive addition<quantity> 2:Multiplication is vector comparison<quality> and on the other side : 3:Division is repetitive subtraction<quantity> 4:Division is vector partition<quality> Thus Fermat is giving us a complementary quantity/quality relationship like the complementary wave/particle relationship in physics. Object lesson : try to simplify and co-ordinate across all science in your search for TRUTH, otherwise the referees may fall asleep before they even finish reading your paper...

Hi to Pasti and Timer-- The paper is published already. I thought people might be interested, or, some people might be interested. I dont think all people will be interested. Most people can understand my proof method, however, it is not difficult. The discussion by timer where three or more terms add up to a fourth term, as I see it, has really nothing to do with the Fermat problem, or not with the problem as stated by Fermat, although you can modify FLT all day and come up with the Beal Conjecture and whatever else, to complicate the matter, or lead to further understandings of Diophantine problems much more complex than the given equation of FLT. FLT uses 2 terms adding up to a third term, in the given equation x^n + y^n = z^n, and I agree with timer that the addition sign is key to solving this; it is key to understand (and is generally just overlooked or not followed up on) that all possible true FLT form equations (including the Pythagorean equations and simple sums of 2 numbers) are of the general form A + B = C; and this can lead to geometric generalization using the Pythagorean diagrams (averaged); then to further analysis--which in my method was by keeping x, y constant, and allowing the n value to vary independently; then finding simultaneous equations and derived graphs. This is the approach I used; and hopefully the method will gain some support and further endorsements.

Well, good. At least we can talk on the same wavelength. As an architect/non-academic, people often ask me : why aren't you a teacher? Ans : the pay is LOUSY and universities are chock full of &%$^#% LIBERALS! Anyway, these 4 laws of qualitative/quantitative math aspects then allowed me to look at multiplication/division in a different way : nx0=? n/0=? Is 2x3x0=6 units of quantity, 6 unit areas or 0 unit volumes? You see, you can get 2 equally valid answers, depending on what you were looking for in the first place : nx0=n+0=n<additive quantities> or nx0=0<vector qualities>. Then, n/0=n-0-0-0-...until the world wears flat and hell glaciates..-0-0-=n<quantitative subtraction> or n/0=infinity<qualitative partition>. Can you divide a radish up into an infinite # of pieces by slicing ZERO pieces off of it? Thus infinity=zero.. Now, lets try nx0=n and n/0=n in this equation : E=mc^2=hw where h is the quantum and w is the matter wavelength<wave #>. If m=0<ie, a momentum state>then it reduces to E=0xc^2=0xw. The speed of a matter wave is given by<where U is the speed of the wave crest> U=c^2/v. That means the waves that accompany fermions travel between c and c^2, but as c^2 AREAS or c^2 LINES? If AREAS you get E=mc^2, if LINES you get c^2x0=c^2<with nx0=n>, or 9x10^16m/s speed limit for fermions<1 light year in 105 seconds> when v=0 in c^2/v<with n/0=n>. Thus, I just gave you the mathematical basis for how aliens in UFOs travel at "warp one" around the universe...and it all comes from figuring out the "secret" of Fermat's Last Theorem...