I have the next equation: $x^2+y^3=n$. Where n is a positive integer constant.


I want to know the exact number of non-negative integer solutions.


Also I want to know what are those solutions. How can I find them?



Non-negative integer solutions of x^2+y^3=n
As mentioned in the comments this is essentially the classic problem of finding integer points of the Mordell curve, and a lot of work has gone into it (for example towards bounding the number of solutions, see [this paper](http://arxiv.org/abs/1405.7022)).


If you want to get understand the basics of the process of finding integers solutions, [this other paper](http://www.inf.unideb.hu/~pethoe/cikkek/67_MORDELL.pdf) works out the $|n|\leq10^4$ range completely (and partially the $|n|\leq10^5$ range).


