On a conjecture of Mordell concerning binary cubic forms

Let f ( x, y ) be a binary cubic form with real coefficients and determinant D ≠ 0. In a recent paper, Mordell has proved that there exist integral values of x, y , not both zero, for which These inequalities are best possible, since they cannot be satisfied with the sign of strict inequality when f ( x, y ) is equivalent to for the case D < 0, or to for the case D > 0.