Let (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1 this is a common divisor section in abstract algebria.
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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...
Originally Posted by Swlabr Let b=c... what if b does not equal c?
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.
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
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