Monday, 3 April 2017

abstract algebra - Does gcd(a,bc) divides gcd(a,b)gcd(a,c)?


I want to prove that gcd divides \gcd(a,b)\gcd(a,c) but I can't succeed.




I tried to go with \gcd(a,b) = sa+tb and it didn't work, tried to use the fact that \gcd(a,b) and \gcd (a,c) divide \gcd (a,bc) but got stuck again.
please help.

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