Establish each of the assertions below:
(a) If a is an arbitrary integer, then 6 | a (a2 + 11).
(b) If a is an odd integer, then 24 | a (a2 − 1).
[Hint: The square of an odd integer is of the form 8k + 1.]
(c) If a and b are odd integers, then 8 | (a2 − b2).
(d) If a is an integer not divisible by 2 or 3, then 24 | (a2 + 23).
(e) If a is an arbitrary integer, then 360 | a2(a2 − 1 )(a2 − 4).
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