Results 1 to 3 of 3

Math Help - Prove that all integers are of the form...

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    1

    Question Prove that all integers are of the form...

    Prove that all integers are of the form 3k, 3k+1, or 3k+2

    The problem is clearly easy and it's obvious why this is true, but I just don't understand how exactly to go about proving it...help?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2010
    Posts
    16
    Because the reminder of division any number by 3 is 0, 1 or 2. so n is 3k+0 or 3k+1 or 3k+2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Black's Avatar
    Joined
    Nov 2009
    Posts
    105
    Follows from the division algorithm (using an integer and 3). For each integer a, there exists unique integers k and r such that

    a=3k+r, where 0 \le r <3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove the sum of all positive integers k...
    Posted in the Number Theory Forum
    Replies: 12
    Last Post: March 2nd 2011, 09:23 AM
  2. Prove 3 divides two integers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 9th 2010, 10:38 AM
  3. prove that the sum of the integers is
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: January 14th 2010, 05:59 AM
  4. Replies: 1
    Last Post: March 4th 2009, 11:06 PM
  5. Replies: 3
    Last Post: December 20th 2008, 10:59 AM

Search Tags


/mathhelpforum @mathhelpforum