1. ## solving big equation...stuck

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

2. If you broke it down correctly then you are left with :

$\displaystyle 2823x + 14811y - 3 = 0$
$\displaystyle 23837x - 5366y - 1 = 0$

(Then solve the system)

EDIT : how could I not think about system of equations ? I lack imagination so badly ...

3. Hello, AwesomeDesiKid!

Find all integer solutions for:
$\displaystyle 67291851x^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3 \:=\:0$

i think i broke it down correctly, but stuck:

. . $\displaystyle (2823x + 14811y - 3)(23837x - 5366y - 1) \:=\:0$

Need (x,y) solutions.

Set each factor equal to zero and solve the system of equations.
(And hope there are integer solutions.)

4. Originally Posted by Soroban
Hello, AwesomeDesiKid!

Set each factor equal to zero and solve the system of equations.
(And hope there are integer solutions.)

The solution set (that is the set of all integer solutions) is $\displaystyle S_1 \cup S_2$ where $\displaystyle S_1$ is the solution set of:

$\displaystyle (2823x + 14811y - 3)=0$

and $\displaystyle S_2$ is the solution set of:

$\displaystyle (23837x - 5366y - 1)=0$

CB

5. Originally Posted by CaptainBlack
The solution set (that is the set of all integer solutions) is $\displaystyle S_1 \cup S_2$ where $\displaystyle S_1$ is the solution set of:

$\displaystyle (2823x + 14811y - 3)=0$

and $\displaystyle S_2$ is the solution set of:

$\displaystyle (23837x - 5366y - 1)=0$

CB
thats the hard part
i been trying to do that for a while and i still haven't figured out how to do it

6. Originally Posted by AwesomeDesiKid
I had the original Equation as
0 = 67291851X^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3
i split it in to
0 = (2823x + 14811y - 3)(23837x - 5366y -1)
then i got

1 = 914x + 4937y
1 = 23837x - 5366y
but i can't slove it, cause i need a x and y as an integers
any help
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
$\displaystyle 0 = 2823x + 14811y - 3$

$\displaystyle y = -\frac{2823}{14811}x + \frac{3}{14811}$
(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
$\displaystyle \left ( 0, \frac{3}{14811} \right )$

-Dan

7. Originally Posted by AwesomeDesiKid
I had the original Equation as
0 = 67291851X^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3
i split it in to
0 = (2823x + 14811y - 3)(23837x - 5366y -1)
then i got

1 = 914x + 4937y
1 = 23837x - 5366y
but i can't slove it, cause i need a x and y as an integers
any help
If you're looking at solving your linear Diophantine equations, here's a site that might help

LINEAR DIOPHANTINE EQUATIONS