What we need here is the fact that every (positive) prime of the form 24n+7 can be (uniquely) represented as a^2 + 6b^2 (a, b are positive (odd) integers). This is true, but I don't have a reference. Anyone? Since 4x^2 - 4xy + 7y^2 = (2x-y)^2 + 6y^2, we just let y = b and x = (a+b)/2. Warut