# Equation of two variables

• Jul 16th 2010, 05:37 AM
Utherr
Equation of two variables
How do i solve this equation of two variables?

I need to find out how many solutions in $\displaystyle \mathbb{Z}\times\mathbb{Z}$ the quation has, $\displaystyle x^4-x^3y-8y^4=0$

I don't know how to solve equations of two or more variables :-s.
• Jul 16th 2010, 07:20 AM
tonio
Quote:

Originally Posted by Utherr
How do i solve this equation of two variables?

I need to find out how many solutions in $\displaystyle \mathbb{Z}\times\mathbb{Z}$ the quation has, $\displaystyle x^4-x^3y-8y^4=0$

I don't know how to solve equations of two or more variables :-s.

By mere inspection, $\displaystyle (2,1)$ is one solution, and since the left hand polynomial is a homogeneous one (of degree 4), $\displaystyle t(2,1)=(2t,t)$ is again a solution for any $\displaystyle t\in\mathbb{Z}$ , so there are infinite (i.e., $\displaystyle \aleph_0$ solutions).

Tonio
• Jul 16th 2010, 07:55 AM
Utherr
So there's no actual calculation here? just thinking? Can you elaborate ? :-s the part after "the left hand polynomial"