Re: FLTAA: Field structure p = 2, p>2


The Dougster wrote:
Chip Eastham wrote:
The Dougster wrote:
Chip Eastham wrote:

Hi, hagman:

Your example:

How about x=2, y=3, z=5, p=5:
Since we have z=y mod x, z=x mod y, x=-y mod z,
it follows that
(z/y,z/x,x/y)^p = (1,1,-1)^5 = (1,1,-1) in Mx x My x Mz.

is of the form x + y = z. In earlier threads the Dougster
restricts interest to 1 < x < y < z < x+y, as solutions
to x^p +y^p = z^p would have z < x+y when p > 1.

Doug was taking an abstract algebra course last term,
as he mentions, and AFAIK his interest in this arose
out his studies.

regards, chip

Hm. I must think more carefully about which restrictions to include
when restating the problem. Like exactly one of x,y,z even. I mean, is
that a restriction or a conclusion?

You ask that x,y,z be pairwise coprime, so that
at most one is even. Having xyz even appears
to be an additional restriction. I was never clear
if you'd found counterexamples with all x,y,z odd.

I agree you should come up with a concise
restatement of the problem with which to lead
off any new thread.

Writing a restatement would be and has been easy. Making it concise is
hard. Would anyone be interested in a wiki for this purpose?

OK!

http://fltma.pbwiki.com/

write for password.

Doug

.

Relevant Pages

  • Re: FLTAA: Field structure p = 2, p>2
    ... Doug was taking an abstract algebra course last term, ... I agree you should come up with a concise ... Writing a restatement would be and has been easy. ...
    (sci.math)
  • Re: FLTAA: Field structure p = 2, p>2
    ... Chip Eastham wrote: ... In earlier threads the Dougster ... Doug was taking an abstract algebra course last term, ...
    (sci.math)
  • Re: FLTAA: Field structure p = 2, p>2
    ... In earlier threads the Dougster ... Doug was taking an abstract algebra course last term, ... when restating the problem. ...
    (sci.math)
  • Re: FLTAA: Field structure p = 2, p>2
    ... In earlier threads the Dougster ... Doug was taking an abstract algebra course last term, ... In other words, the minimal exponent. ...
    (sci.math)