Derive each of the following congruences:
(a) a21 ≡ a (mod 15) for all a.
[Hint: By Fermat’s theorem, a5 ≡ a (mod 5).]
(b) a7 ≡ a (mod 42) for all a.
(c) a13 ≡ a (mod 3 · 7 · 13) for all a.
(d) a9 ≡ a (mod 30) for all a.
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