Prove the assertions below:
(a) If a is an odd integer, then a2 ≡ 1 (mod 8).
(b) For any integer a, a3 ≡ 0, 1, or 6 (mod 7).
(c) For any integer a, a4 ≡ 0 or 1 (mod 5).
(d) If the integer a is not divisible by 2 or 3, then a2 ≡ 1 (mod 24).
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