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Can someone please help me solve this? I am absolutely bamboozled!

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So that's sort of a wacky set of premises.  For example, if I am reading that right, the middle one says the gcd of three integers all greater than 1 never exists.  Then the first one makes another odd claim about prime numbers.

The best I can suggest it to see if you can use those three given premises to construct the conclusion, or not.  You'll note the similarity of the second premise and the conclusion.

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