Newsgroups: sci.math
From: haoyuep@aol.com (Dan Hoey)
Date: 2000/03/14
Subject: Re: Mr Benschop ad nauseam

Robin Chapman writes:
>Let's look at the 27 Dec 1999 version of Benschop's non-proof
>of FLT.

>Page 8.[...]

Nice.  I didn't get that far.  But it's startling how badly he could botch
Theorem 3.1.  As written, it's a restatement of the definition.  I amused
myself by proving the slightly nontautological:

  For invertible elements a,b,c of a ring with identity, consider the four
  statements:
    P.  a + b^-1 = -1
    Q.  b + c^-1 = -1
    R.  c + a^-1 = -1
    S.     a b c = 1
  Then any two of these statements imply the others.

It's not hard to prove this by trial and error, though I suspect there's an
effective method (is it a Grobner thing?).  But Benschop writes down the
four statements and doesn't say what he's proving.  Can we guess what
he's proving from the proof? He reasons that that given S we have
P=>Q=>R=>P, but then he concludes S!

Dan Hoey
haoyuep@aol.com