Thread: divisibility proof

The question I am working on is
Prove that a/b if and only if a^3/b^3.

I know that if p/a^n then p/a...but how can i apply that here..can i make a prime on my own despite the question did not say?

Originally Posted by empressA

The question I am working on is
Prove that a/b if and only if a^3/b^3.

I know that if p/a^n then p/a...but how can i apply that here..can i make a prime on my own despite the question did not say?

I'm pretty sure we can go through with bi-implications this way.

for some



since

and done.


Now if that makes you uncomfortable, and you want to do both directions, change all the above 's to 's and consider that your proof of the forward direction.

For the backwards direction, you will need to work a little harder. Personally, I'd do a proof by contradiction, employing the division algorithm.