a^2+b^2=c^3, a,b,c are positive integers, and b>=a.
Just by inspection, a=b=c=2 is one set of solution.
Also, a=26, b=18, c=10; a=1358, b=594, c=130; are two other sets of solutions.
If you multiply a and b by n^3 and c by n^2 for any positive integers n, you can easily get related sets of solutions.
So my the question is:
- Do other solutions exists?
- Are there any solutions, such that a,b,c are pairwise coprime, exists?