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 and all the , and then use the fact that does not have any prime factor in common with any of the , and therefore neither with .