[seqfan] Re: Finding numbers represented by indefinite binary quadratic forms

[Neil Sloane]

Dave, Thanks, that Mathematica command does indeed seem to do the job! It
gives (as you say) a long list of solutions if solutions exist, and "false"
if they don't.
Neil


On Wed, Jun 4, 2014 at 10:02 AM, David Applegate <david at research.att.com>
wrote:

> This is not my field, so I may be misunderstanding, but as I understand it,
> these second-order bivariate Diophantine equations are studied under the
> scope of generalized Pell's equations.  The mathworld page on them,
> http://mathworld.wolfram.com/PellEquation.html, claims that
> the Mathematica command Reduce[f[x,y], {x,y}, Integers] finds
> solutions when they exist.  (It also claims another form, but I think
> that has a typo).
>
> For example, in Mathematica,
>
> Reduce[x^2 - 3 x y - 3 y^2 - 15 == 0, {x,y}, Integers]
>
> gives a pile of general solutions.
>
> The mathworld page
> http://mathworld.wolfram.com/DiophantineEquation2ndPowers.html has a
> moderate discussion.
>
> -Dave
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com