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Need help with this math problem!! Prove: For all a,b,c in the integers, if (a,b)=1 and c divides a+b, then (a,c)=1 and (b,c)=1.?

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Need help with this math problem!! Prove: For all a,b,c in the integers, if (a,b)=1 and c divides a+b, then (a,c)=1 and (b,c)=1.?

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