Can You Solve These Prime Number Proofs?

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    Prime Proofs
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Homework Help Overview

The discussion centers around two questions related to prime numbers: proving that if \((2^d) - 1\) is prime, then \(d\) must also be prime, and proving that \((p-1)C(k)\) is congruent to \((-1)^k \mod p\). Participants are seeking assistance with these proofs.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are encouraged to share their attempts and where they are encountering difficulties. One participant suggests that if \(d\) is even, then \((2^d) - 1\) cannot be prime, leading to an indirect proof approach.

Discussion Status

The discussion is ongoing, with participants requesting more details about the original poster's attempts. Some guidance has been offered regarding the nature of the first question, but there is no explicit consensus on the approaches to take.

Contextual Notes

There is a note that the questions may be more appropriate for a different section of the forum, indicating potential constraints on where the discussion should take place.

JdotAckdot
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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
 
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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.
 
JdotAckdot said:
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.
 
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.
 

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