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

[David Applegate]

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