1. ## divisibility proof

Prove that if k and n are positive integers and k divides n, then $\displaystyle 2^k-1$ divides $\displaystyle 2^n-1$.

I feel like I've done this problem before, but I'm not sure how to approach it.

2. Originally Posted by jmedsy
Prove that if k and n are positive integers and k divides n, then $\displaystyle 2^k-1$ divides $\displaystyle 2^n-1$.

I feel like I've done this problem before, but I'm not sure how to approach it.
Since k divides n, n = kl for some positive integer l.

Use the fact that $\displaystyle x-1$ divides $\displaystyle x^m - 1$ for any positive integer $\displaystyle m$

Choose $\displaystyle x = 2^k$ and $\displaystyle m = l$ in the above statement to get your answer.

3. Originally Posted by Isomorphism
Since k divides n, n = kl for some positive integer l.

Use the fact that $\displaystyle x-1$ divides $\displaystyle x^m - 1$ for any positive integer $\displaystyle m$

Choose $\displaystyle x = 2^k$ and $\displaystyle m = l$ in the above statement to get your answer.
I understand, thanks.