Results 1 to 6 of 6

Math Help - Norms and primes

  1. #1
    Junior Member
    Joined
    Apr 2008
    From
    Gainesville
    Posts
    68

    Norms and primes

    I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.
    Last edited by JCIR; April 29th 2008 at 08:04 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by JCIR View Post
    I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.
    How do you define the norm of a+b\sqrt{p}?

    Is it \sqrt{a^2 + b^2}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    From
    Gainesville
    Posts
    68

    norms and prime number

    The norm is defined by N(a+bsqrt(p))= /a^2-pb^2/
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Is p prime ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2008
    From
    Gainesville
    Posts
    68

    norms and primes

    p is prime or -1
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by JCIR View Post
    I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.
    Consider \mathbb{Z}[i] and then any prime p\equiv 3(\bmod 4) is a Gaussian prime and its norm is p^2 - not a prime.

    More specifially, 3\in \mathbb{Z}[i] and N(3) = 9 with 3 being irreducible.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. norms on R
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 10th 2011, 02:42 PM
  2. [SOLVED] Norms in R^m
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: February 26th 2011, 08:51 PM
  3. Primes in Z[i] with norms less than 26?
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: October 20th 2010, 09:42 AM
  4. Replies: 12
    Last Post: September 22nd 2010, 02:43 AM
  5. vector norms and matrix norms
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 13th 2010, 02:42 PM

Search Tags


/mathhelpforum @mathhelpforum