if gcd(a,b)=1 then gcd(a^3,b^3)=
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Similarly, if p|b, then b⧸|a+b. Thus we conclude p=3. But then if 9|gcd(a+b,3ab), clearly 3|a or 3|b and again 3⧸|a+b. Since gcd(a,b)=1 hence gcd(a+b,a)=1 and gcd(a+b,b) = 1
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