Re: Fermat's Lost Proof

talkjunk@xxxxxxxxxxx wrote:

Oops. Using "x" vs "+" was just stupid and was simply an oversite of
the most basic kind. Many apologies. Using "x" vs "*" resulted from
conversion from a real word processor to plain text. I also hate the
inability to use subscripts and superscripts thus my desire to post
this to arXiv.org.

The term did translate as "marvelous" so there's a minor semantic
difference and it is not clear if he was being extremely sarcastic or
only slightly sarcastic about the proof not fitting into the margin.

I have no idea if I will find what Fermat claimed he found. More than
likely not, but it is quite fun looking. I probably belong to the group
of people that believe he actually had a proof - elegant or marvelous
or not.

Thanks for the comments.

Tim



I've just lately worked through the posts in this thread, which is fascinating.
I'm left unclear, though, on what, in your scheme, distinguishes the case
n=2 from all others. You write that the set of intervals "intersects" the
power series. Are you referring to the fact that all odd squares will occur
in the set of all odd numbers (which is the set of first-order intervals
for n=2)? This is certainly true, but how does the fact that 2!=2 relate to
this intersection?

I write to ask this because something significant seems to be lurking in
your discovery that all intervals between equal powers of different
integers can be equated to arithmetic expressions consisting of the same
powers of other integers multiplied by coefficients from Pascal's Triangle,
plus the factorial of the power in question.  If you could establish
that the presence of the factorial prevents, in each case for n>2,
the expressions from representing  integers to the power n, then
you would have a proof of FLT remarkably shorter than the presently
known ones.  There would have to be something special about the
particular integers which appear in your expressions, otherwise any
integer to the power n could trivially be represented by n! followed
by sufficiently many occurences of 1 to the power n.

.

Relevant Pages

  • Re: Question about Sun JAVAC
    ... > I suspect you mean BNF? ... I'm not In The Least interested in typing BNF expressions ... > mention all the power contained in a small space. ... > OTOH, when I'm designing a mini-language or grammar, I use BNF. ...
    (comp.programming)
  • Re: Frameworks
    ... Werkzueg leave more control in the users hands hopefully leading to ... greater expression and power. ... DAL expressions translate one-to-one into SQL statements in the ... Of course you can more complex expressions for nested selects, joins, ...
    (comp.lang.python)
  • Re: May I introduce myself to cobol?...
    ... >> I think Cobol language have the power, ... > limitations' while actually using expressions that include CALL ... ... "Obviously" these cannot be used in the RETURNING or BY REFERENCE phrases. ...
    (comp.lang.cobol)
Quantcast