Results 1 to 5 of 5

Math Help - explanation of quadratic residue

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    4

    explanation of quadratic residue

    I'm having trouble understanding the concept of quadratic residue. I know you are supposed to take the integers lower than your mod number and square them and reduce via the mod number. My question is how do you know if you have a solution? For example 2^2 \equiv 4(mod 13) is not a solution but 3^2 \equiv 9(mod 13) is a solution. I don't understand why one is and not the other. Both 4 and 9 are squares of an integer. I know I'm misunderstanding something fundamnetal but I can't find any simple answers in my book or on the net. Thanks for any help.
    David
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by drounds67 View Post
    I'm having trouble understanding the concept of quadratic residue. I know you are supposed to take the integers lower than your mod number and square them and reduce via the mod number. My question is how do you know if you have a solution? For example 2^2 \equiv 4(mod 13) is not a solution but 3^2 \equiv 9(mod 13) is a solution. I don't understand why one is and not the other. Both 4 and 9 are squares of an integer. I know I'm misunderstanding something fundamnetal but I can't find any simple answers in my book or on the net. Thanks for any help.
    David
    Both 4 and 9 are quadratic residues modulo 13. For a complete list, see Quadratic residue.
    Last edited by alexmahone; April 28th 2011 at 10:56 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    4

    explanataion

    I know I can look them up on a list but that didn't answer my question. Let me try to phrase it better. I'm trying to determine the procedure to know what values are the quadratic residues of (mod 13). so I can repeat the method on a test or quiz with a different modulus.
    thanks
    david
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by drounds67 View Post
    I know I can look them up on a list but that didn't answer my question. Let me try to phrase it better. I'm trying to determine the procedure to know what values are the quadratic residues of (mod 13). so I can repeat the method on a test or quiz with a different modulus.
    thanks
    david
    Considering mod 13,

    1^2\equiv1

    2^2\equiv4

    3^2\equiv9

    4^2\equiv3

    5^2\equiv12

    6^2\equiv10

    7^2\equiv(-6)^2\equiv10
    .........................
    .........................
    12^2\equiv(-1)^2\equiv1

    Therefore, the quadratic residues modulo 13 are 1, 4, 9, 3, 12 and 10.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2011
    Posts
    4
    thanks. I got it now, it makes sense. I think the way the notes were written was throwing me off.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. When is 2 a quadratic residue?
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: February 8th 2011, 06:49 PM
  2. Quadratic residue -5
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: March 10th 2010, 02:35 PM
  3. Quadratic Residue
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: November 25th 2009, 09:36 PM
  4. quadratic non residue
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 13th 2009, 10:36 AM
  5. law of quadratic residue
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 9th 2008, 10:53 AM

Search Tags


/mathhelpforum @mathhelpforum