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## Homework Statement

Let a,b,c be integers. If (b,c)=1, then (a,bc)=(a,b)(a,c)

## Homework Equations

This is difficult to answer because some theorems that we haven't proven yet, we can't use.

## 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.