Results 1 to 4 of 4

Thread: Show that there exists a unique element c of Z such that n divides ab-c

  1. #1
    Member
    Joined
    Feb 2017
    From
    N/A
    Posts
    91

    Exclamation Show that there exists a unique element c of Z such that n divides ab-c

    Let n be a positive integer. Define Zn = {0, 1, 2, ..., n-1}. Let a, b ∈ Zn. Show that there exists a unique element of c of Zn, such that n divides ab-c.

    OK. This is the question translated in words. Let n be a positive integer. Define Z sub n to be equal to the set {0, 1, 2, ..., n-1}. Let a, b be elements of set Z sub n. Show that there exists a unique element of c of Z sub n, such that n divides (a times b) minus c.

    This question I am beyond lost, especially since our prof just gave us this problem with no examples to compare it to. I feel like you have to take some arbitrary element and somehow manipulate via proof to show that n divides ab-c.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    668
    Thanks
    304

    Re: Show that there exists a unique element c of Z such that n divides ab-c

    we divide ab by n to get a quotient q and remainder c
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2017
    From
    N/A
    Posts
    91

    Re: Show that there exists a unique element c of Z such that n divides ab-c

    But how does this relate to the original question of showing that "there exists a unique element"? Or is what you have there sufficient?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    668
    Thanks
    304

    Re: Show that there exists a unique element c of Z such that n divides ab-c

    a b=n q+c

    0\leq  c < n

    c\in  \mathbb{Z}_n and n divides a b - c

    c is the number we are looking for

    we need to show that it is the unique such number
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Dec 15th 2012, 07:08 PM
  2. Replies: 3
    Last Post: Oct 8th 2011, 04:16 PM
  3. Replies: 2
    Last Post: May 1st 2011, 02:11 PM
  4. unique element y of S that satisfies...
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Apr 21st 2010, 05:56 AM
  5. Replies: 5
    Last Post: Apr 3rd 2010, 06:10 PM

Search tags for this page


/mathhelpforum @mathhelpforum