Find all values of n that solve each of the following equations.
(a) φ(n) = n/2
(b) φ(n) = n/3
(c) φ(n) = n/6
[Hint. The formula in Exercise might be useful.]
Exercise:
(a) For each integer 2 ≤ a ≤ 10, find the last four digits of a1000.
(b) Based on your experiments in (a) and further experiments if necessary, give a simple criterion that allows you to predict the last four digits of a1000 from the value of a.
(c) Prove that your criterion in (b) is correct.
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