# Thread: Prove or disprove that (ac,b) =1

1. ## Prove or disprove that (ac,b) =1

Let (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1

this is a common divisor section in abstract algebria.

2. Originally Posted by rainyice
Let (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1

this is a common divisor section in abstract algebria.
Let b=c...

3. Originally Posted by Swlabr
Let b=c...
what if b does not equal c?

4. Originally Posted by rainyice
what if b does not equal c?
That doesn't matter. This provides a counter example.

If you want to look more into this problem, use the fact that a|b implies that there is an x such that ax=b.

5. Originally Posted by Swlabr
That doesn't matter. This provides a counter example.

If you want to look more into this problem, use the fact that a|b implies that there is an x such that ax=b.

I chose a=11 b=4 and c=8 so that (ac,b) is not equal to 1 but (a,b) and (a,c) are equal to 1