1.(a) Do there exist integers a, b, c such that gcd(a, b) = 30, gcd(b, c) = 24, gcd(a, c) = 54? Prove or disprove. (b) Do there exist integers x, y, z such that gcd(x, y) = 30, gcd(x, z) = 24, gcd(y, z) = 84? Again, prove or disprove.

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