# composite

• January 27th 2009, 05:06 PM
Sally_Math
composite
prove that n is composite, then 2^(n)-1 is composite.

I need a prove, but I just want to know can I also prove using a counter example.
• January 27th 2009, 06:46 PM
ThePerfectHacker
Quote:

Originally Posted by Sally_Math
prove that n is composite, then 2^(n)-1 is composite.

I need a prove, but I just want to know can I also prove using a counter example.

Hint: $x^m - 1 = (x-1)(x^{n-1}+x^{n-2}+...+x+1)$.
Now assume that $n=ab$ and consider $\left( 2^a\right)^b - 1$ and expand.