Proving any odd number is a factor of $2^n -1$ for some $n$ I'm struggling with a proof of the following. I feel like it should be a one-liner or something simple but I'm just not grasping the idea:
Suppose that m is an odd natural number. Prove that there is a natural number $n$ such that $m$ divides $2^n -1$
Any help would be much appreciated, thanks.

$$(2k+1) \mid 2^{\phi(2k+1)} -1 $$ 
by http://en.wikipedia.org/wiki/Euler%27s_theorem
