I am new here, and still don't know how to make the tex and type the same size, or provide titles to links to URL's to my pdf; I would appreciate help. That said,
I have a proof of Fermat's Last Theorem (unlike Wiles' Theorem) that I'd like to present in this thread.
The Binomial Expansion
is everything that is not
would almost seem to be a proof by inspection. If it is mapped to a single value, the inspection would make it clear that in the equation
, would mean that for Fermat's equation
to hold, then
, which in turn means that
to be single valued.
Note that in Fermat's expression there are no products of the type
, so that his expression is actually a metric for a Presburger arithmetic. The integers are based on Peano's axioms which does include multiplication, as does the Binomial Expansion. IMO, this is actually a proof of Gödel's theorem, where an arithmetic system without multiplication is not complete, but if it is complete, then it must include non-integers (real and complex)
However, there are subtleties; In my paper, I show how the Special Theory of Relativity creates the field of positive real numbers, of which the integers are a subset from ct=0. For binomials (The Binomial Expansion also applies to positive real numbers), two relativistic circles are necessary as final states (to "reified" real numbers, valid for the final field by adjusting
. The two circles are required so that independent (a,b) be established on the positive integer plane; again, emphasizing that Fermat's expression does not include multiplicative products such as ab for independent integers (a,b).
(The relativistic unit circles form the bases for the Dirac gamma zero matrix in QFT).
I have two core papers (both of which are works in progress) dealing with this approach with URL's as well as associated update documents with additional details. I would be very interested in discussing them with an open mind I have written a short summary. I do assume that any responder will be interested in the equations (and interpretations of them), and will be open to reading links to Wiki if I provide them...
(Important; m proof is based on the existence of a binomial; that is, two dimensions each with a field, not just one as the number theorists I am familiar insist on discussing, rejecting Descartes from the start... :) This stuff isn't easy for me or anyone else, and sometimes one has to sit quietly in a dark room and think a bit before responding.
If someone will show me how to create a URL where I can title it instead of using the actual URL, I will proved links to both papers and updates for review and discussion.
Thanks for listening; I look forward to an intelligent discussion. And if I'm wrong (or it has already been done), then it still will move the ball forward for me...