Results 1 to 2 of 2

Thread: Quadratic primes

  1. Oct 21st 2006, 02:28 AM #1
    beta12
    beta12 is offline
    Member
    Joined
    Sep 2006
    Posts
    83

    Quadratic primes

    Question 1)
    Prove that there are infinitely many prime in Q[sqrt(d)] .
    Hint: It is almost identical to the proof that there are infinitely many prims in Z.

    Question 2)
    Find a prime factorization of 6 in Q[ sqrt(-1)] ?

    Hi Perfecthacker,
    Could you please teach me how to solve these questions? Thank you very much.
    Follow Math Help Forum on Facebook and Google+
  2. Oct 21st 2006, 04:04 PM #2
    ThePerfectHacker
    ThePerfectHacker is offline
    Global Moderator
    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Question 2)
    Find a prime factorization of 6 in Q[ sqrt(-1)] ?
    We can non-trivally factor 6 as 2*3.
    Now,
    2=(1+i)(1-i)
    But three cannot be factored because it is not of the form 4k+1.
    Thus,
    6=3(1+i)(1-i)
    Follow Math Help Forum on Facebook and Google+
« Quadratic integers | fermat...or not fermat? »

Similar Math Help Forum Discussions

  1. Primes that are quadratic residues another prime.
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: Dec 16th 2011, 02:10 PM
  2. odd primes p for which 7 is a quadratic residue mod p
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Mar 31st 2011, 12:04 PM
  3. Primes in Quadratic Fields
    Posted in the Number Theory Forum
    Replies: 31
    Last Post: Sep 9th 2010, 02:09 PM
  4. Primes in Quadratic Fields
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Oct 4th 2008, 06:06 PM
  5. Primes in quadratic field
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Sep 28th 2008, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum