Use the Gaussian integers to find the solutions in rational integers of the diophantine equation x^2+1=y^3

a) Show that if x and y are integers such that x^2+1=y^3, then x - i and x + i are relatively prime

b) Show that there are integers r and s such that x= r^3 - 3r*(s^2) and 3*(r^2)*s-s^3=1

c) Find all solutions in integers x^2+1=y^3 by analyzing the equations for r and s in part (b)