if (a,b)=d and (a,b^n)=d' find the relationship between d and d'?

Question

anonymous · Answer

interesting question

anonymous · Answer

$$a)d \le d' <d^n$$$$b)d'=d^n$$$$c)d'>d$$$$d'<d^n$$

anonymous · Answer

if $(a,b)=1$ then for sure $(a,b^n)=1$ aswell

zzr0ck3r · Answer

how in the word could you possibly say that?

anonymous · Answer

way what? that is was interesting?

loser66 · Answer

I don't get it.!! the question is about the relationship between d and d'. Among the choices, only one option shows the relationship between them. Do we need any other logic to get the answer??

anonymous · Answer

good point !

zzr0ck3r · Answer

I was saying I do not understand how we can make any conclusion about anything given the information. :)

I do agree it is interesting. We just cant assume that $=1$ is even a thing because the relation $\le $ seems to be on the ordered pairs. 

:)

ganeshie8 · Answer

Are you sure the first option isn't
$a)~d \le d' \color{red}{\le} d^n$

?

freckles · Answer

I think the fundamental theorem of arithmetic is useful here if anyone needs any convincing
 
(think prime factorizations )