Are the cube roots of two integers chosen from a uniform distribution between $1$ and $p-1$ inclusive, $p$ prime, essentially evenly distributed? Note that I will use a $p$ such that $p$ is not equivalent to $2$ modulo $3$.
In other words, I'm trying to ensure that if I pick a random number between $1$ and $p-1$ I will have an equal chance of that number being the cube of some integer.
I've searched the site for answers, but my search did not come up with anything, and I don't know enough theory, except for maybe trying to read more on cubic reciprocity.
I've found a similar result for square roots here.