I need to find ALL INTEGER solutions for
0 = 67291851x^2 + 337901589xy − 79475826y^2 − 74334x + 1287y + 3
i think i broke it down correctly, but stuck
= (2823x + 14811y − 3)(23837x − 5366y − 1)
need (x,y) solutions
Nice job factoring. I have no idea how you did that.
You aren't going to get a set (x, y) for these. From the first factor you get
(I'll let you take care of the cancellations.)
This linear relationship gives you a list of zeros of this equation. The other factor gives you a similar solution.
You may, of course, pick out a specific zero. For example, we can pick out x = 0 and we have the zero
-Dan
If you're looking at solving your linear Diophantine equations, here's a site that might help
LINEAR DIOPHANTINE EQUATIONS