Hi, I have the following problem in a course titled "Introduction to Abstract Algebra"... I am not quite sure if I got the question right though because it looks so easy.

Thanks for your help!

"Prove that the equation

$\displaystyle x^6+7y^3=2$

has no solution with x and y being in Z (set of integers)"

I think that is it because $\displaystyle y=(2-x^6)^{1/3}/(7)^{1/3}$...but I don't know how to explain it :-/