Question: Let a and b be integers not both 0. Prove that if gcd(a, 4) = gcd(b, 4) = 2, then gcd(a+b, 4) = 4.

Let a and b be integers not both 0. Prove that if gcd(a, 4) = gcd(b, 4) = 2, then gcd(a+b, 4) = 4.

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