Results 1 to 2 of 2

Math Help - Gauss Lemma (Number Theory)

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    5

    Gauss Lemma (Number Theory)

    Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}).

    I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as:

    (\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges between 1 and \frac{(p-1)}{2}, n is the number of minus signs that occur in this way. I don't understand how to use this form of Gauss's Lemma
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by mathsss2 View Post
    Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}).

    I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as:

    (\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges between 1 and \frac{(p-1)}{2}, n is the number of minus signs that occur in this way. I don't understand how to use this form of Gauss's Lemma
    In \{ 6,12,18,24,30,36\} the corresponding remainders are \{6, -1, 5, -2, 4, -3 \}.
    There are 3 negative signs.
    Therefore, (6/13) = (-1)^3 = -1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 07:09 PM
  2. Lebesgue's Number Lemma
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 10th 2011, 08:59 AM
  3. Gauss' Lemma and algebraic integers
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: May 25th 2010, 09:23 PM
  4. primitive, Gauss Lemma
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: January 23rd 2009, 01:58 AM
  5. Number Theory - Eulers Criterion and Gauss' Lemma
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: August 11th 2007, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum