16th Canadian Mathematical Olympiad Problems 1984

16th Canadian Mathematical Olympiad Problems 19841.  Show that the sum of 1984 consecutive positive integers cannot be a square. 2.  You have keyring with n identical keys. You wish to color code the keys so that you can distinguish them. What is the smallest number of colors you need? [For example, you could use three colors for eight keys: R R R R G B R R.