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Give an example of three positive integers m, n, and r, and three integers a, b, and c such that the GCD of m,

 

Give an example of three positive integers m, n, and r, and three integers a, b, and c such that the GCD of m, n, and r is 1, but there is no simultaneous solution to x = a (mod m) = b (mod n) x = c (mod r). Justify that your example satisfies the requirement.

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