Results 1 to 7 of 7

Math Help - Jacobi Symbol

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    12

    Jacobi Symbol

    Last edited by milfner; May 5th 2008 at 08:44 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by milfner View Post
    Use the fast computation method without factoring (except for removing 2ís) to determine the Jacobi symbol (13925 / 3927611)


    Mention all formulas you apply as you apply them
    (13925/3927611) = (3927611/13925) = (761/13925) = (13925/761) = (227/761) = (761/227) = (80/227) = (5/227) = (227/5) = (2/5) = -1

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    12
    Last edited by milfner; May 5th 2008 at 08:45 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by milfner View Post
    Thanks for your reply. Can you please show me how you got the answer...
    Explain which steps you cannot follow.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2008
    Posts
    12
    All of them
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    The Jabobi symbol is a generalization of the Legendre symbol. Given two integers a,b where b>1 and odd. Define (a/b) = (a/p_1)...(a/p_m) where b=p_1...p_m is a factorization of not necessarily distinct primes (here the RHS is the regular Legendre symbol).

    Here are some simple properties.
    • (a_1/b) = (a_2/b) if a_1\equiv a_2(\bmod b)
    • (2/b) = (-1)^{(b^2-1)/8}
    • (a_1a_2/b) = (a_1/b)(a_2/b)
    • (a/b)(b/a) = (-1)^{(a-1)/2\cdot (b-1)/2} where a is odd and > 1


    All of these were used. Figure out which ones.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Mar 2008
    Posts
    12
    Last edited by milfner; May 5th 2008 at 08:45 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Jacobi Symbol Properties
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: April 15th 2010, 06:08 PM
  2. Jacobi Symbol
    Posted in the Number Theory Forum
    Replies: 12
    Last Post: March 8th 2010, 08:53 PM
  3. Jacobi identity
    Posted in the Math Challenge Problems Forum
    Replies: 11
    Last Post: October 8th 2009, 12:20 AM
  4. [SOLVED] Jacobi Symbol
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 13th 2008, 07:52 PM
  5. Jacobi identity
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: August 6th 2006, 08:08 PM

Search Tags


/mathhelpforum @mathhelpforum