Prove the following statements:
(a) For any integer a, the units digit of a2 is 0, 1, 4, 5, 6, or 9.
(b) Any one of the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 can occur as the units digit of a3.
(c) For any integer a, the units digit of a4 is 0, 1, 5, or 6.
(d) The units digit of a triangular number is 0, 1, 3, 5, 6, or 8.
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