Equation of two variables

**Utherr** · July 16th 2010, 05:37 AM

How do i solve this equation of two variables?

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

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

**tonio** · July 16th 2010, 07:20 AM

Originally Posted by Utherr

How do i solve this equation of two variables?

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

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

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

Tonio

**Utherr** · July 16th 2010, 07:55 AM

So there's no actual calculation here? just thinking? Can you elaborate ? :-s the part after "the left hand polynomial"

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