Authors: Allen D Allen
By proving that his “last theorem” (FLT) is true for the integral exponent n = 3, Fermat took the first step in a standard method of proving there exists no greatest lower bound on n for which FLT is true, thus proving the theorem. Unfortunately, there are two reasons why the standard method of proof is not available for FLT. First, transitive inequality lies at the heart of that method. Secondly, FLT admits to a change from > to < rendering their transitive natures unavailable. A related, self evident symmetry illustrates another problem that would have plagued Fermat and centuries of successors. FLT asserts such a narrow proposition, it is difficult to find an antecedent while easy to find a non equivalent consequence. For example, if FLT asserted that the exponent n is even, then FLT would be equivalent to the proposition that Fermat’s equation has two solutions, one for positive bases and one for their negative counterparts. This could be addressed with conservative transformations. The example provided by FLT motivates the use of an early paper by the author to prove a theorem on theorems. The theorem on theorems demonstrates there are infinitely many theorems as difficult to prove as FLT.
Comments: Abstract contains 200 words, ms runs 6 pages
Unique-IP document downloads: 52 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.