Homework Help: Prime proofs

1. Nov 3, 2005

JdotAckdot

Just a couple questions that I'd appreciate any help on.

1. if [(2^d) - 1] is prime, prove that d is prime as well.

2. Prove that (p-1)C(k) is congruent to (-1)^k mod p.

I've started them both but ended up getting stuck.
Any ideas?

Thanks

2. Nov 4, 2005

Gokul43201

Staff Emeritus
1. These look like textbook questions and so should go into the appropriate section of the Science Education Zone.

2. To get help, you must first show what you've tried and where you're stuck.

3. Nov 5, 2005

Tom Mattson

Staff Emeritus
Yes, show us how you started and where you got stuck. The responses by CarlB and AKG have been "soft deleted" and will be restored once you have shown an attempt at the problem.

4. Nov 13, 2005

shravan

first Q is simple

if d is even .2^d is 2^2n .even no: are {expressed in this form } ie 4^n if n is prime i.e. n>or=2 4^n is > or = 16. 4^n -1 is never a prime no. { eg 16-1=15}
so n cannot be even.thus we can prove by indirect method.