# Need help doing a proof

• October 20th 2008, 08:57 PM
noles2188
Need help doing a proof
Prove:
If a positive integer n is not prime, then 2^(n)-1 is not prime.

If n is not prime, then it factors into n = a*b. Use the identity
x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).
• October 21st 2008, 12:25 AM
Opalg
Quote:

Originally Posted by noles2188
Prove:
If a positive integer n is not prime, then 2^(n)-1 is not prime.

If n is not prime, then it factors into n = a*b. Use the identity
x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).

There's a "-1" missing in that identity. It should be $x^b {\color{red}{} - 1} = (x-1)(x^{b-1} + x^{b-2} + \ldots + x + 1)$. Substitute $x=2^a$ in that and you should have no trouble getting the result.