a) Show that if a, b, and c are integers with (a,b)=(a,c)=1, then (a,bc)=1.

b) Use mathematical induction to show that if a1, a2,.....,an are integers, and b is another integer such that (a1,b)=(a2,b)=...=(an,b)=1, then(a1a2...an, b)=1

Thanks for your help.