Question: Let a; b; c be positive integers such that a 2 + b 2 = c 2 . Give a counterexample or proof to each

Let a; b; c be positive integers such that a2 + b2 = c2. Give a counterexample or proof to each of the following.

(a) a or b is even.

(b) 3 divides a or 3 divides b

(c) 5 divides at least one of a, b, or c.

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