Results 1 to 4 of 4

Math Help - Proof: Sum of three odd numbers is odd.

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    ct
    Posts
    5

    Proof: Sum of three odd numbers is odd.

    How do I start?

    I know that an odd number can be defined at 2K+1. Would I suppose the result is odd?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Proof: Sum of three odd numbers is odd.

    I would begin by letting the three odd numbers be:

    x=2k_1+1

    y=2k_2+1

    z=2k_3+1

    where k_i\in\mathbb{Z}

    and so:

    x+y+z=?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    ct
    Posts
    5

    Re: Proof: Sum of three odd numbers is odd.

    I think I figured it out. x = (2K+1) y = (2J+1) z = (2Q+1) = 2K+2J+2Q+3 (Factor out 2)

    so, 2 (K+J+Q) + 1 is odd by definition and Axiom 2.

    Yes?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Proof: Sum of three odd numbers is odd.

    A small point...you should have after factoring, x + y + z = 2(K + J + Q + 1) + 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Numbers Proof
    Posted in the Advanced Math Topics Forum
    Replies: 4
    Last Post: October 22nd 2012, 12:45 PM
  2. Numbers - a very basic proof
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 14th 2012, 01:05 PM
  3. Proof: All rational numbers are algebraic numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 5th 2010, 10:26 AM
  4. rational numbers proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 6th 2009, 12:33 AM
  5. Proof Perfect Numbers
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 29th 2007, 01:11 PM

Search Tags


/mathhelpforum @mathhelpforum