Prove or disprove that (ac,b) =1

• Mar 2nd 2010, 10:14 PM
rainyice
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.
• Mar 2nd 2010, 11:39 PM
Swlabr
Quote:

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...
• Mar 3rd 2010, 06:50 AM
rainyice
Quote:

Originally Posted by Swlabr
Let b=c...

what if b does not equal c?
• Mar 3rd 2010, 09:12 AM
Swlabr
Quote:

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.
• Mar 8th 2010, 04:07 PM
rainyice
Quote:

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