Problem: Give a proof or a counterexample for the following.

- If a^n|b^n then a|b

Thought I had a solution in here, but it didn't work. I received help though, so I know what to do now. Thanks!

Since we can assume a^n|b^n, we can write x*a^n=b^n. Then we can rewrite as:

a^(n-1)*a*x=b^(n-1)*b

(a^(n-1)/b^(n-1))*x*a=b

From here I tried to say that a^(n-1)/b^(n-1) was an integer, using a^n|b^n. More evidence I have been doing too much math, and my brain is shutting down.

I know what to do now, I just had to correct this so it didn't look like I was a complete idiot.