Results 1 to 2 of 2

Math Help - equation mod 195

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    142

    equation mod 195

    What's the quickest way to solve x^3 = 38 (mod 195)?

    I see that 195 = 3*5*13
    I think I should use the Chinese Remainder Theorem.
    I find that
    in mod 3, the solution is 2,
    in mod 5, the solution is 2,
    in mod 13, the solutions are 4,10,12.
    So there should be 3 solutions to the given problem. However, I don't know how to proceed from here. The cubic part and the fact that I can break it up into 3 primes is a little different than the other ones in the text.

    Thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by PvtBillPilgrim View Post
    What's the quickest way to solve x^3 = 38 (mod 195)?

    I see that 195 = 3*5*13
    I think I should use the Chinese Remainder Theorem.
    I find that
    in mod 3, the solution is 2,
    in mod 5, the solution is 2,
    in mod 13, the solutions are 4,10,12.
    So there should be 3 solutions to the given problem. However, I don't know how to proceed from here. The cubic part and the fact that I can break it up into 3 primes is a little different than the other ones in the text.
    Just treat it as three separate problems. You can combine the first two congruences to say x\equiv2\!\!\!\pmod{15}. Now use the CRT to find a solution mod 195 for each of these three problems:

    (i) x\equiv2\!\!\!\pmod{15},\quad x\equiv4\!\!\!\pmod{13},

    (ii) x\equiv2\!\!\!\pmod{15},\quad x\equiv10\!\!\!\pmod{13},

    (iii) x\equiv2\!\!\!\pmod{15},\quad x\equiv12\!\!\!\pmod{13}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  2. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM
  3. Replies: 2
    Last Post: May 18th 2009, 12:51 PM
  4. Replies: 2
    Last Post: April 28th 2009, 06:42 AM
  5. Replies: 1
    Last Post: October 23rd 2008, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum