Results 1 to 4 of 4

Math Help - Positive integers in a binomial relation

  1. #1
    Newbie Demandeur's Avatar
    Joined
    Jun 2010
    Posts
    14

    Positive integers in a binomial relation

    Determine all {m, n}\in\mathbb{N} such that \displaystyle \binom{n+1}{m+1} = \binom{n+1}{m} = \frac{5}{3} \binom{n+1}{m-1}.
    Last edited by Demandeur; September 5th 2010 at 09:39 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    Quote Originally Posted by Demandeur View Post
    Determine all {m, n}\in\mathbb{N} such that \displaystyle \binom{n+1}{m+1} = \binom{m+1}{m} = \frac{5}{3} \binom{n+1}{m-1}.
    Should there be an n in your second binomial coefficient?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie Demandeur's Avatar
    Joined
    Jun 2010
    Posts
    14
    Quote Originally Posted by chiph588@ View Post
    Should there be an n in your second binomial coefficient?
    In fact, Cliph, yes. Thank you. I've edited now. I'm sorry for any trouble which that might have caused. Strange enough, I remember double-checking.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Demandeur View Post
    Determine all {m, n}\in\mathbb{N} such that \displaystyle \binom{n+1}{m+1} = \binom{n+1}{m} = \frac{5}{3} \binom{n+1}{m-1}.
    We can first get rid of the trivial cases where all are 0; ie, m-1 > n+1. Then I believe the first equation implies that n is even and m=n/2. Then since the sequence of C(n+1,m)/C(n+1,m-1) for n = {2,4,6,...} and m=n/2 is strictly decreasing, the unique other solution is given by (n,m) = (6,3).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: January 30th 2010, 04:59 AM
  2. if x and n are positive integers....
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 7th 2009, 12:07 AM
  3. no positive integers
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 7th 2009, 10:51 AM
  4. Positive Integers
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: May 31st 2007, 02:48 PM
  5. Sum of Positive Integers
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 31st 2007, 05:34 AM

Search Tags


/mathhelpforum @mathhelpforum