Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By SlipEternal

Math Help - Proofs Involving Congruence of Integers

  1. #1
    Junior Member
    Joined
    Sep 2013
    From
    United States
    Posts
    67
    Thanks
    3

    Proofs Involving Congruence of Integers

    Course: Foundations of Higher Math

    Let
    n\in Z. If n^2 \not \equiv n(mod3), then n \not \equiv 0(mod3) and n \not \equiv 1(mod3). State and prove the converse.

    Converse: If n \not \equiv 0(mod3) and n \not \equiv 1(mod3), then n^2 \not \equiv n(mod3).

    It seems easier to prove by contrapositive so

    Assume that n^2 \equiv n(mod3), i.e. n^2 - n = 3a, for some integer a.

    \Rightarrow n(n-1)=3a \Rightarrow (n-0)(n-1)=3a

    So, 3|(n-0) or 3|(n-1).

    Hence, n \equiv 0(mod3) or n \equiv 1(mod3)

    How's that?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,765
    Thanks
    683

    Re: Proofs Involving Congruence of Integers

    Looks good to me
    Thanks from MadSoulz
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proofs using real numbers and integers
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: September 8th 2011, 06:58 PM
  2. Replies: 1
    Last Post: November 2nd 2009, 08:00 PM
  3. Congruence Proofs: Summations
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: October 28th 2009, 09:41 AM
  4. Proofs-Divisibility of Integers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 14th 2009, 11:45 PM
  5. congruence and quadratic integers.
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: October 26th 2006, 05:19 AM

Search Tags


/mathhelpforum @mathhelpforum