Results 1 to 2 of 2

Math Help - Solving a linear congruence

  1. #1
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241

    Solving a linear congruence

    Hi again,

    From practice questions for upcoming test:

    Solve the linear congruence: 4x \equiv 5 (mod 11)

    First find the inverse, 11 = (2)(4) + 3; 4 = (1)(3) + 1

    so 3 = 11 + (-2)(4) and 1 = 4 - 3 = 4 - [ (1)(11) + (-2)(4)] = (-1)(11) + (3)(4)

    So 4(3) \equiv 1 (mod 11) and 4(15) \equiv 5 (mod 11)

    Therefore the solution is x = 15.

    Is the above correct? Or since 15 -11 = 4 and 0 < 4 < 11, would 4 be a more correct answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by oldguynewstudent View Post
    Hi again,

    From practice questions for upcoming test:

    Solve the linear congruence: 4x \equiv 5 (mod 11)

    First find the inverse, 11 = (2)(4) + 3; 4 = (1)(3) + 1

    so 3 = 11 + (-2)(4) and 1 = 4 - 3 = 4 - [ (1)(11) + (-2)(4)] = (-1)(11) + (3)(4)

    So 4(3) \equiv 1 (mod 11) and 4(15) \equiv 5 (mod 11)

    Therefore the solution is x = 15.

    Is the above correct? Or since 15 -11 = 4 and 0 < 4 < 11, would 4 be a more correct answer?

    Not more correct, but undoubtedly nicer and more widely accepted since we're used to take zero and the naturals up to 10 as the representative of the residues modulo 11.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Congruence
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 24th 2010, 05:11 AM
  2. Solving a congruence equation.
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 31st 2009, 05:22 AM
  3. solving congruence equations
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 9th 2009, 02:17 PM
  4. Linear congruence
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 1st 2009, 05:48 AM
  5. Solving a congruence
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 15th 2008, 09:10 AM

Search Tags


/mathhelpforum @mathhelpforum