If gcd(a, b)=1 then prove that gcd(a^n,b^n)=1.

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If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1 If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1