32nd British Mathematical Olympiad 1996 Problems

32nd British Mathematical Olympiad 1996 Problems1.  Find all non-negative integer solutions to 2m + 3n = k2. 2.  The triangle ABC has sides a, b, c, and the triangle UVW has sides u, v, w such that a2 = u(v + w - u), b2 = v(w + u - v), c2 = w(u + v - w). Show that ABC must be acute angled and express the angles U, V, W in terms of the angles A, B, C.