Re: rational solution to a bivariate polynomial

In article
<1190327520.710962.142100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
,
David Stahl <pavco@xxxxxxxxxxxxx> wrote:

I am hoping someone can point me to a
source that discusses my problem. I am trying to
find a rational
solution for x and y to the equation:

Ax^2 + Bxy + Cy^2 + Dx + Ey + F =0 (1)


where the coefficients are rational. This can be
transformed to:


xprm^2 - d*yprm^2 + N = 0 (2)


There are alot of websites that talk about finding
integer solutions
to these equations with integer coefficients. I do
not think an
integer solution always exists when the
coefficients are
rational but I do think a rational solution always
does exist and I
am
perfectly happy with a rational solution. Any
guidance would be
appreciated. Thank you.

I think you'll find the equation x^2 - 3y^2 + 1 = 0
has no rational solutions.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for
email)

perhaps if we extend the OP's conjecture to "gaussian rationals"

gaussian rationals = gaussian integers / integers

regards
tommy1729
.

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