Thread: 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).

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 . Substitute in that and you should have no trouble getting the result.