Using the fundamental basis of the field L 9 = Q(2 cos(π/9)), the form N L9 (γ) = f (x, y, z) is found and the Diophantine equation f (x, y, z) = a is solved. A similar scheme is used to construct the form N L7 (γ) = g(x, y, z). The Diophantine equation g(x, y, z) = a is solved.