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Let a, b, c, m be integers with m > 0. Prove the following: (a) ”a...

Let a, b, c, m be integers with m > 0. Prove the following: (a) ”a ≡ 0 (mod 2) if and only if a is even” and ”a ≡ 1 (mod 2) if and only if a is odd”. (b) a ≡ b (mod m) if and only if a − b ≡ 0 (mod m) (c) a ≡ b (mod m) if and only if (a mod m) = (b mod m). Recall from Definition 8.10 that (a mod m) denotes the remainder when dividing a by m. (d) a ≡ b (mod 2) if and only if a and b have the same parity.

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