Can You Solve These Prime Number Proofs?

[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

 

[Gokul43201]

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.

 

[quantumdude]

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

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.

 

[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.