# Math Help - prove tha if k/n

1. ## prove tha if k/n

Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)

2. Originally Posted by mandy123
Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)
In general if $k|n$ then $a^k-1$ divides $a^n-1$.
This is because $n=km$ thus $a^{km}-1 = (a^k)^m - 1$.
Now use identity for factoring $x^n - y^n$.