24th Canadian Mathematical Olympiad Problems 1992

24th Canadian Mathematical Olympiad Problems 19921.  Show that n! is divisible by (1 + 2 + ... + n) iff n+1 is not an odd prime. 2.  Show that x(x - z)2 + y(y - z)2 ≥ (x - z)(y - z)(x + y - z) for all non-negative reals x, y, z. When does equality hold?