Re: what is this problem all about...
- Not to say that this makes it "easy," but I thought the Catalan
conjecture was resolved about a year and a half ago. A Google
search found http://www.ams.org/bull/2004-41-01/S0273-0979-03-00993-
5/S0273-0979-03-00993-5.pdf as an AMS Bulletin summarizing the
On the other hand I tested out to .... oh shoot, I cut and pasted
something over the cut and pasted number that I had searched up to
but it is started with a 2 and many digits, like 2 million or 2
billion. Darn darn darn. Oh well, not any more solutions for a
long long time.
--- In email@example.com, mikeoakes2@a... wrote:
> I wrote
> >Perhaps someone would like to use Pari to settle this question?
> I asked David Broadhurst for help on this and, guru that he is, he
has come up with the goods. To quote his email:-
> >Magma V2.11-6
> >Sun Oct 3 2004 11:26:59 on modular [Seed = 2793930133]
> > -------------------------------------
> > 1
> > Total time: 0.190 seconds, Total memory usage: 3.50MB
> So, the rank is indeed 1, and all rational solutions are of the
form p_n = n*P_1.
> Now "all" that remains is to show that the denominator of the x
and y coordinates of P_n are never 1, for n > 6.
> Ideas, anyone?
> [This part is going to be /hard/: as David pointed out, the
Catalan problem (a^2=b^3+1) is of the same type, and has so far
resisted all attempts at a solution.]
> -Mike Oakes