1. The problem statement, all variables and given/known data Let a,b,c be integers. If (b,c)=1, then (a,bc)=(a,b)(a,c) 2. Relevant equations This is difficult to answer because some theorems that we haven't proven yet, we can't use. 3. The attempt at a solution Let g=(a,b) and h=(a,c), g and h are integers. That means g|a and g|b, h|a and h|c. That means: a=gk, for some integer k b=gq, for some integer q a=hp for some integer p c=ht for some integer t. Multiply b and c together to get bc=(a,b)(a,c)qt. Then (a,bc)= (gk, (a,b)(a,c)qt), but that's as far as I got.