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Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod...

Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod m2) if and only if (meaning prove both ways) a ≡ b (mod m1m2). Hint: If a | bc and a is relatively prime to to b then a | c.

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