Math question - factoring a bivariate polynomial

[Andrew Plewe]

I have a question related to an algorithm and several sequences I'm working
on. Feel free to answer off-list and only if you have some spare time to do
so.

Let us assume you have the following polynomial:

a.) x^2 - ax - 2xy - by + c = 0

Assume that a, b, and c are large (>80 digits) composite integers whose
factorizations are known. I wish to find valid values for x and y. Is it
easier to factor the polynomial directly, or to find solutions to:

b.) x^2 - ax - 2xy + c = 0 modulo b

And then search within those values for x,y which satisfy eqn a?

Thanks for your time!

	-Andrew Plewe-