1. Prove that for every , 133 divides
2. An integer n is a perfect square if it is the square of some other integer.
(For example 1, 4, 9, 16, 25 and 36 are all perfect squares.) Prove by induction that the sum 1 + 3 + 5 + 7 + ... + 2n-1 (i.e. the sum of the first n odd integers) is always a perfect square.
Can you give a "geometric proof"?
3. Show that for any 2n x 2n board with one square deleted can be covered by Triominoes.