I have seen this equation $y^3 - 3x^2 = p^m$ to determine the solutions. I know this is elliptic curve. I had some knowledge of elliptic curve. But, I was totally upset to determine the solutions of this kind equation. what are the best possible ways to find solutions of such equations? Then I will find solutions of $y^5 - 5x^2 = p^m$, once I know the method to find solutions of $y^3 - 3x^2 = p^m$. Where $p$ is prime and $x, y, m$ are some positive integers.