relatively prime problem

• April 29th 2009, 12:57 PM
htata123
relatively prime problem
Hi,

Need help with this problem;

Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

Prove that

(a,b1b2....bn) = 1

Thanks
• April 30th 2009, 07:13 AM
Prime factors
Hello htata123
Quote:

Originally Posted by htata123
Hi,

Need help with this problem;

Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

Prove that

(a,b1b2....bn) = 1

Thanks

You need to consider the (unique) prime factorisation of $a$ and all the $b_i$, and then use the fact that $a$ does not have any prime factor in common with any of the $b_i$, and therefore neither with $\prod{b_i}$.