Which condition is necessary for ax2+by2+cz2=0ax^2 + by^2 + cz^2 = 0ax2+by2+cz2=0 to have non-trivial integer solutions?
−ab-ab−ab is a quadratic residue mod ccc
All a,b,ca, b, ca,b,c must be positive
−bc-bc−bc is a quadratic residue mod aaa
a,b,ca, b, ca,b,c must be coprime