# Integer solutions for #x^3 - 3 x y^2 + 2 y^3=2017# ?

##### 2 Answers

#### Answer:

The solution is the set of points (x, y ) on the graph. for

#### Explanation:

The x-intercept is #(2017)^(1/3)=12.635, nearly.

y-intercept ; #(2017/2)^(1/3)=10.028, nearly.

The graph depicts the solution set {( x, y ) }. It seems that there are

asymptotes given by (x-y)(x+2y)=0, in proximity.

graph{(x^3-3xy^2+2y^3-2017)(x-y)(x+2y) =0 [-49.5, 49.5, -24.75, 24.75]}

#### Answer:

#### Explanation:

We will looking for solutions

This is a homogeneous equation. So doing

so

but

or

The solution is given by the first system and is