Equation with an infinite number of solutions I have the following equation: $x^3+y^3=6xy$. I have two questions: 1. Does it have an infinite number of rational solutions? 
2. Which are the solutions over the integers?($ x=3 $ and $ y=3 $ is one)
Thank you!

The equation is symmetric in $x$ and $y,$ suggesting solutions of the form $x=y.$ Plugging that in, we find $$2x^3-6x^2=0$$ This gives the solution $x=y=0.$ 
Simplifying by dividing by $2x^2$ gives $x-3=0,$ leading to another solution $x=y=3.$ 
