26th Eötvös Competition Problems 1922

1.  Show that given four non-coplanar points A, B, P, Q there is a plane with A, B on one side and P, Q on the other, and with all the points the same distance from the plane. 2.  Show that we cannot factorise x4 + 2x2 + 2x + 2 as the product of two quadratics with integer coefficients.