x^3+y and y^3+x are divisible by x^2+y^2 gcd(x,y)=d Let’s is divisible by p^k and wlog x and d aren’t divisible by p^{k+1}. Then y^3 is divisible by p^{3k} and x^2+y^2 is divisible by p^{2k}. So, x is divisible by p^{2k}, so k=0. That is, d=1. x^2 is equivalent to -y^2, therefore -y^2x+y and -x^2y+x are divisible by x^2+y^2 Since, x and y are coprime with x^2+y^2 1-xy is divisible by x^2+y^2 But |1-xy |<|x^2+y^2|, except of x=0 or y=0 So, answer is (1,0);(0,1);(1,1);(-1,-1).