Find all integer solutions of y² = x³ - 432.

(In reply to

This is to the author. by Vee-Liem Veefessional)

Vee-Liem Veefessional asked:

Is this Keplar's Law??!! If I am not not wrong, I am referring to his third law..??

No.

Kepler's third law states that: "*The square of the sidereal period of an orbiting planet is directly proportional to the cube of the orbit's semimajor axis.*"

So Kepler's third law states that the square of one quantity is proportional to the cube of another, *in the context of planetary orbits.* On the other hand, this puzzle asks for two *integers*, such that the square of one is 432 greater than the cube of the other.